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UNIVERSITY  OF  CALIFORNIA. 


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Works  of  Prof.  Robt,  H.  Tkurston, 

Published   by  JOHN   WILEY  &  SONS,   53   E.  Tenth 
Street,   New  York. 


MATERIALS  OF  ENGINEERING. 

A  work  designed  for  Engineers,  Students,  and  Artisans  in  wood, 
metal,  and  stone.  Also  as  a  TEXT-BOOK  in  Scientific  Schools,  show- 
ing the  properties  of  the  subjects  treated.  By  Prof.  R.  H.  Thurston. 
Well  illustrated.  In  three  parts. 

Part  I.    THE  NON-METALLIC  MATERIALS  OF  ENGINEER 

ING  AND  METALLURGY. 

With  Measures  in  British  and  Metric  Units,  and  Metric  and  Reduction 
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Part  II.    IRON  AND   STEEL. 

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(  >]>per.  Tin,  Zinc,  Lead,  Antimony,  Bismuth,  Nickel,  Aluminum,  etc.; 
The  Brasses,  Bronzes;  Copper-Tin-Zinc  Alloys;  Other  Valuable 
Alloys;  Their  Qualities,  Peculiar  Characteristics;  Uses  and  Special 
Adaptations;  Thurston's  "Maximum  Alloys";  Strength  of  the 
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MATERIALS  OP  CONSTRUCTION. 

A  Text-book  for  Technical  Schools,  condensed  from  Thurston's 
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especially  brasses  and  bronzes,  and  their  "kalchoids":  strength, 
ductility,  resistance,  and  elasticity,  effects  of  prolonged  and  oft- 
repeated  loading,  crystallization  and  granulation;  peculiar  metals: 
Thurston's  "maximum  alloys";  stone;  timber;  preservative  pro- 
cesses, etc.,  etc.  By  Prof.  Robt.  H.  Thurston,  of  Cornell  University. 

Many  illustrations Thick  8yo,  cloth,    500 

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is  a  sufficient  guarantee  for  its  accuracy  and  thoroughness."—  Building. 

TREATISE   ON  FRICTION  AND  LOST  WORK  IN  MACHIN- 
ERY AND  MILL  WORK. 

Containing  an  explanation  of  the  Theory  of  Friction,  and  an  account 
of  the  various  Lubricants  in  general  use,  with  a  record  of  various 
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etc.  By  Prof.  Robt.  H.  Thurston.  Copiously  illustrated.  .8vo,  cloth,  :j  1*1 

"It  is  not  too  high  praise  to  say  that  the  present  treatise  is  exhaustive 
and  a  complete  review  of  the  whole  subject." — American  Engineer. 

STATIONARY    STEAM-ENGINES. 

Especially  adapted  to  Electric  Lighting  Purposes.  Treating  of  the 
Development  of  Steam-engines— the  principles  of  Construction  and 
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gines. By  Prof.  R.  H.  Thurston 12mo,  cloth.  1  30 

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users  of  steam-engines ." — Builder  and  Wood-worker. 


DEVELOPMENT    OF    THE    PHILOSOPHY   OF   THE    STEAM- 
ENGINE. 

By  Prof.  11.  H.  Thurston 12mo,  cloth,  $0  75 

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would  want,  and  at  the  same  time  a  succinct  account  covering  so  much 
ground.as  to  be  of  great  value  to  the  specialist."— Public  Opinion. 
A  MANUAL  OF  STEAM  BOILERS,   THEIR  DESIGNS,  CON- 
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For  Technical  Schools  and  Engineers.    By  Prof.  R.  H.  Thurston.    (183 

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STEAM-BOILER  EXPLOSIONS  IN  THEORY  AND  IN  PRAC- 
TICE. 

Containing  Causes  of— Preventives— Emergencies— Low  Water— Con- 
sequences—Management—  Safety—  Incrustation  —  Experimental  In- 
vestigations, etc.,  etc.,  etc.  By  R.  H.  Thurston,  LL.D.,  Dr.  Eng., 
Director  of  Sibley  College,  Cornell  University.  With  many  illus- 
trations  12mo,  cloth,  150 

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"  It  is  a  work  that  might  well  be  in  the  hands  of  every  one  having  to  do 
with  steam  boilers,  either  in  design  or  use." — Engineering  News. 
A  HAND  BOOK  OF  ENGINE    AND    BOILER    TRIALS,    AND 

THE  USE  OF  THE  INDICATOR  AND  THE  BRAKE. 
By  R.  H.  Thurston,  Director  of  Sibley  College,  Cornell  University. 

Second  edition  revised 5  00 

"Taken  altogether,  this  book  is  one  which  every  Engineer  will  find  of 
value,  containing,  as  it  does,  much  information  in  regard  to  Engine  and 
Boiler  Trials  which  has  heretofore  been  available  only  in  the  form  of  scat- 
tered paper:*  in  the  transactions  of  engineering  societies,  pamphlet  reports, 
note-books,  etc."—  Railroad  Gazette. 
CONVERSION  TABLES. 

Of  the  Metric  and  British,  or  United  States  WEIGHTS  AND  MEAS- 
URES. With  an  Introduction  by  Robt.  H.  Thurston,  A.M.,  C.E. 

8vo,  cloth,    1  00 

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and  unfamiliarity  of  the  Metric  System  renders  such  a  volume  as  this  almost 
indispensable  to  Mechanics,  Engineers,  Students,  and  in  fact  all  classes  of 
people."— Mechanical  News. 
REFLECTIONS  ON  THE  MOTIVE  POWER  OF  HEAT. 

And  on  Machines  fitted  to  develop  that  Power.  From  the  original 
French  of  N.  L.  S.  Carnot.  By  Prof.  R.  H.  Thurston —  12mo,  cloth,  2  00 

From  Mons.  Haton  de  la  Goupilliere,  Director  of  they  Ecole  Naiionale 
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ment pour  r Industrie  Nntiowile: 

"  I  have  received  the  volume  so  kindly  sent  me,  which  contains  the  trans- 
lation of  the  work  of  Carnot.    You  have  rendered  tribute  to  the  founder  of 
the  science  of  thermodynamics  in  a  manner  that  will  be  appreciated  by  the 
whole  French  people." 
A  MANUAL  OF  THE  STEAM  ENGINE. 

A  companion  to   the  Manual  of   Steam  Boilers.     By  Prof.  Robt. 

H.  Thurston.    2  vols «vo,  cloth,  12  00 

Part  I.    HISTORY,  STRUCTURE  AND  THEORY. 

For  Engineers  and  Technical  Schools.    (Advanced  courses.)    Nearly 

900  pages «vo,  cloth,    7  50 

Part  II.    DESIGN,  CONSTRUCTION  AND  OPERATION. 

For  Engineers  and  Technical  Schools.     (Special  courses  in  Steam 

Engineering.) 8vo,  cloth,    7  50 

TEXT-BOOK  OF  THE  PRIME  MOTORS. 

For  the  Senior  Year  in  Schools  of  Engineering.  By  Prof.  R.  H. 
Thurston.  Ready,  Fall  of  '92. 


HANDY   TABLES, 


FROM  THURSTON'S  STEAM-ENGINE  MANUAL 


FOR  USE  IN  LABORATORY  COMPUTATIONS 
IN  TECHNICAL  SCHOOLS. 


NUMERICAL,  TRIGONOMETRICAL,    AND    THERMODYNAMIC  QUANTITIES; 
STEAM  AND   HORSE-POWER  TABLES,   AND  RECORD- 
FORMS   FOR  LABORATORY   USE 


UNIVERSITY 


NEW  YORK: 
JOHN  WILEY  &  SONS, 

53  EAST  TENTH  STREET. 
1891. 


COPYRIGHT,  1891, 

BY 
B.  H.  THURSTON. 

7  5-££  5" 


HANDY  TABLES, 

FROM  THURSTON'S  STEAM-ENGINE  MANUAL. 


PAGE 

I.  NUMERICAL  CONSTANTS;  CIRCLES;  AREAS;  ETC 4 

II.  LOGARITHMS,  COMMON  AND  NATURAL 17 

III.  MEAN  PRESSURE  RATIOS 20 

IV.  TERMINAL  PRESSURES 23 

V.  HEAT  TRANSFER  AND  TRANSFORMATION 24 

VI.  COMPARISON  OF  THERMOMETERS 26 

VII.  VOLUMES  OF  WATER;  DENSITIES 28 

VIII.  METRIC  STEAM  TABLE 29 

IX.  METRIC  STEAM  AND  WORK  TABLE 32 

X.  STEAM  TABLE;  BRITISH  UNITS 34 

XI.  STORED  ENERGY  IN  STEAM  AND  WATER 41 

XII.  FORMULAS  FOR  PROPERTIES  OF  STEAM 43 

XIII.  FACTORS  OF  EVAPORATION 45 

XIV.  COMPOSITION  OF  FUELS 46 

XV.  HORSE-POWER  CONSTANTS 48 

XVI.  REAL  RATIOS  OF  EXPANSION 49 

XVII.  LOGS  AND  FORMS  FOR  BLANKS 50 

XVIII.  ELECTRICAL  HORSE-POWER 54 

XIX.  WATER  COMPUTATION  TABLE 55 

XX.  HIRN'S  ANALYSIS  BLANKS 57 

XXI.  HEAT  AND  POWER  UTILIZATION;  NON-CONDENSING  ENGINE 59 


HANDY   TABLES. 


I. 


NUMERICAL  CONSTANTS. 


n 

«7T 

«•? 

4 

»' 

«3 

V» 

h 

.O 

3.142 

0.7854 

1.  000 

I.OOO 

.0000 

.0000 

.1 

3.456 

0.9503 

I.  210 

1.331 

.0488 

.0323 

.2 

3-770 

I.I3IO 

1.440 

1.728 

.0955 

.0627 

•  3 

4.084 

1-3273 

1.690 

2.197 

.1402 

.0914 

•4 

4-398 

1-5394 

1.960 

2.744 

.1832 

.1187 

•  5 

4.712 

1.7672 

2.250 

3.375 

.2247 

.1447 

.6 

5.027 

2.OI06 

2.560 

4.096 

.2649 

.1696 

•  7 

5.341 

2  .  2698 

2.890 

4-913 

.3038 

•I()3S 

.8 

5.655 

2-5447 

3.240 

5.832 

.3416 

.2164 

•9 

5.969 

2.8353 

3-610 

6.859 

.3784 

.2386 

2.0 

6.283 

3.T4I6 

4.000 

8.000 

.4142 

•2599 

2.1 

6-597 

3.4636 

4.410 

9.261 

.4491 

.2806 

2.2 

6.912 

3.8013 

4.840 

10.648 

.4832 

.3006 

2-3 

7.226 

4.1543 

5.290 

12.167 

.5166 

.3200 

2.4 

7.540 

4.5239 

5.760 

13-824 

.5492 

.3389 

2.? 

7.854 

4.9087 

6.250 

15-625 

.5811 

•3572 

2.6 

8.168 

5.3093 

6.760 

17-576 

.6125 

•  3751 

2.7 

8.482 

5.7256 

7.290 

19.683 

.6432 

•3925 

2.8 

8.797 

6.1575 

7.840 

21.952 

.6733 

.4095 

2.9 

9.111 

6.6052 

8.410 

24-389 

.7029 

.4260 

3.0 

9.425 

7.0686 

9-00 

27.000 

.7321 

.4422 

3-i 

9.739 

7-5477 

9.6l 

29.791 

•  7607 

.4581 

3-2 

10.053 

8.0425 

10.24 

32.768 

.7889 

.4736 

3-3 

10.367 

8.5530 

10.89 

35-937 

.8166 

.4888 

3-4 

10.681 

9.0792 

11.56 

39-304 

.8439 

.5037 

3-5 

v   10.996 

9.6211 

12.25 

42.875 

.8708 

.5183 

3-6 

11.310 

10.179 

12.96 

46.656 

.8974 

•5326 

3-7 

11.624 

10.752 

13.69 

50.653 

•9235 

.5467 

3.8 

n.938 

11.341 

14.44 

54.872 

.9494 

-5605 

3-9 

12.252 

11.946 

15.21 

59-3I9 

.9748 

•5741 

4.0 

12.566 

12.566 

I6.OO 

64.000 

2.0000 

.5874 

4.1 

12.881 

13.203 

16.81 

68.921 

2.O249 

.6005 

4.2 

13.195 

13-854 

17.64 

74.088 

2.0494 

.6134 

4-3 

13-509 

14.522 

18.49 

79.507 

2.0736 

.6261 

4.4 

13-823 

15-205 

19.36 

85.184 

2.0976 

.6386 

4-5 

14.137 

15.904 

20.25 

91-125 

2.I2I3 

1.6510 

4-6 

14.451 

16.619 

21.  16 

97.336 

2  .  1448 

1.6631 

4-7 

14-765 

17-349 

22.09 

103.823 

2.1680 

i  6751 

HANDY   TABLES. 
CONSTANTS — Continued. 


n 

MT 

""* 

«* 

»' 

¥1 

fc 

4-8 

15.080 

18.096 

23.04 

110.592 

2.1909 

.6869 

4.9 

15-394 

18.857 

24.01 

117.649 

2.2136 

.6985 

5-0 

15-708 

19-635 

25.00 

125.000 

2.2361 

.7100 

5-i 

16.022 

20.428 

26.01 

132.651 

2.2583 

.7213 

5.2 

16.336 

21.237 

27.04 

140.608 

2.2804 

.7325 

5-3 

16.650 

22.062 

28.09 

148.877 

2.3022 

.7435 

5-4 

16.965 

22.902 

29.16 

157.464 

2.3238 

•7544 

5-5 

17.279 

23.758 

30.25 

166.375 

2.3452 

.7652 

5-6 

17.593 

24.630 

31-36 

175-616 

2.3664 

.7758 

5-7 

17.907 

25-518 

32-49 

185.193 

2-3875 

.7863 

5-8 

18.221 

26.421 

33-64 

195-112 

2.4083 

•7967 

5-9 

18.535 

27-340 

34.81 

205.379 

2.4290 

.8070 

6.0 

18.850 

28.274 

36.00 

216.000 

2.4495 

.8171 

6.1 

19.164 

29.225 

37.21 

226.981 

2.4698 

.8272 

6.2 

19.478 

30.191 

38.44 

238.328 

2.4900 

-8371 

6.3 

19.792 

3I-I73 

39-69 

250.047 

2.5100 

.8469 

6.4 

20.106 

32.170 

40.96 

262  .  144 

2.5298 

.8566 

6.5 

20.420 

33-183 

42.25 

274.625 

2-5495 

.8663 

6.6 
6.7 

20.735 
21.049 

34.212 

35.257 

43-56 
44-89 

287.496 
300.763 

2.5691. 

2.5884 

.8758 
.8852 

6.8 

21.363 

36-317 

46.24 

314.432 

2.6077 

•  8945 

6.9 

21.677 

37-393 

47.61 

328.509 

2.6268 

.9038 

7.0 

21.991 

38-485 

49-00 

343.000 

2.6458 

.9129 

7.1 

22.305 

39-592 

50.41 

357.9" 

2.6646 

.9220 

7.2 

22.619 

40.715 

51.84 

373-248 

2.6833 

.9310 

7.3 

22.934 

41.854 

53.29 

389-017 

2.7019 

•9399 

7-4 

23.248 

43.008 

54.76 

405.224 

2.7203 

.9487 

7-5 

23.562 

44.179 

56.25 

421.875 

2.7386 

•  9574 

7.6 

23.876 

45.365 

57.76 

438.976 

2.7568 

.9661 

7-7 

24.190 

46.566 

59-29 

456.533 

2-7749 

•  9747 

7-8 

24.504 

47.784 

60.84 

474-552 

2.7929 

.9832 

7-9 

24.819 

49.017 

62.41 

493.039 

2.8107 

.9916 

8.0 

25.133 

50.266 

64.00 

512.000 

2.8284 

2.0000 

8.1 

25.447 

51.530 

65.61 

53L44I 

2.8461 

2.0083 

8.2 

25.761 

52.810 

67.24 

55L468 

2.8636 

2.0165 

8.3 

26.075 

54.106 

68.89 

57L787 

2.8810 

2.0247 

8-4 

26.389 

55.418 

70.56 

592  .  704 

2.8983 

2.0328 

8-5 

26.704 

56.745 

72.25 

614.125 

2.9155 

2.0408 

8.6 

27.018 

58.088 

73.96 

636.056 

2.9326 

2.0488 

8-7 

27-332 

59-447 

75.69 

658.503 

2.9496  ' 

2.0567 

8.8 

27.646 

60.821 

77-44 

681.473 

2.9665 

2.0646 

8.9 

27.960 

62.211 

79.21 

704.969 

2.9833 

2.0724 

HANDY   TABLES. 
CONSTANTS — Continued. 


n 

tilt 

*»? 

4 

»» 

«3 

V* 

s 

*'« 

9  ° 

28.274 

63.617 

Sl.OO 

729.000 

3.0000 

2.0801 

Q.I 

28.588 

65.039 

82.81 

753-571 

3.0166 

2.0878 

9.2 

28.903 

66.476 

84.64 

778.688 

3.0332 

2.0954 

9-3 

29.217 

67.929 

86.49 

804.357 

3.0496 

2.1029 

9-4 

29.531 

69.398 

88.36 

830.584 

3.0659 

2.1105 

9-5 

29.845 

70.882 

90.25 

857.375 

3.0822 

2.1179 

9.6 

30.159 

72.382 

92.16 

884.736 

3.0984 

2.1253 

9-7 

30.473 

73.898 

94.09 

912.673 

3.1145 

2.1327 

9.8 

30.788 

75.430 

96.04 

941.192 

3.1305 

2.1400 

9-9 

31.102 

76.977 

98.01 

970.299 

3.1464 

2.1472 

10.  0 

31.  4r6 

78.540 

IOO  .  OO 

1000.000 

3.1623 

2.1544 

10.  1 

31.730 

So.Iig 

102.01 

1030.301 

3.1780 

2.1616 

re.  2 

32.044 

81.713 

104.04 

1061.208 

3.1937 

2.1687 

10.3 

32.358 

83.323 

106.09 

1092.727 

3.2094 

2.1757 

10.4 

32.673 

84.949 

108.16 

1124.863 

3-2249 

2.1828 

10.5 

32.987 

86  .  590 

110.25 

1157.625 

3.2404 

2.1897 

10.6 

33.301 

88.247 

112.36 

1191.016 

3-2558 

2.1967 

10.7 

33.615 

89.920 

114.49 

1225.043 

3.2711 

2  .  2036 

10.8 

33.929 

91.609 

116.64 

1259.712 

3.2863 

2.2IO4 

10.9 

34-243 

93.313 

118.81 

1295.029 

3.3015 

2.2172 

II.  0 

34-558 

95.033 

121.00 

1331.000 

3.3166 

2.2239 

li.  i 

34.872 

96.769 

123.21 

1367.631 

3.3317 

2.2307 

II.  2 

35-186 

98.520 

125.44 

1404.928 

3.3466 

2.2374 

II-  3 

35  •  500 

100.29 

127.69 

1442.897 

3.3615 

2.2441 

11.4 

35.814 

102.07 

129.96 

1481.544 

3.3764 

2.25O6 

ii.  5 

36.128 

103.87 

132.25 

1520.875 

3-39*2 

2.2572 

11.  6 

36.442 

105.68 

134.56 

1560.896 

3-4059 

2.2637 

II-  7 

36.757 

107.51 

136.89 

1601.613 

3.4205 

2.27O2 

II.  8 

37.071 

109.36 

139.24 

1643.032 

3.4351 

2.2766 

11.9 

37.385 

III.  22 

141.61 

1685.159 

3.4496 

2.2831 

12.0 

37.699 

II3.IO 

144.00 

1728.000 

3.4641 

2.2894 

12.  1 

38.013 

114.99 

146.41 

1771.561 

3.4785 

2.2957 

12.2 

38.327 

116.90 

148.84 

1815.848 

3.4928 

2.3021 

12.3 

38.642 

II8.82 

151.29 

1860.867 

3.5071 

2.3084 

12.4 

38.956 

120.76 

153.76 

1906.624 

3.5214 

2.3146 

12.5 

39-270 

122.72 

156.25 

1953.125 

3-5355 

2.3208 

12.6 

39-584 

124.69 

158.76 

2000.376 

3.5496 

2.3270 

12.7 

39-898 

126.68 

161.29 

2048.383 

3.5637 

2-3331 

12.8 

40.212 

128.68 

163.84 

2097.152 

3-5777 

2.3392 

12.9 

40.527 

130.70 

166.41 

2146.689 

3.5917 

2-3453 

13.0 

40.841 

132.73 

169.00 

2197.000 

3.6056 

2.3513 

13.1 

4LI55 

134.78 

171.61 

2248.091 

3-6194 

2-3573 

13.2 

41.469 

136.85 

174.24 

2299.968 

3.6332 

2.3633 

HANDY   TABLES. 
CONSTANTS — Continued. 


* 

MT 

*** 

4 

»» 

*' 

V~n 

fa 

13  3 

4L783 

138.93 

176.89 

2352.637 

3-6469 

2.3693 

13-4 

42.097 

I4L03 

179.56 

2406.104 

3.6606 

2-3752 

13-5 

42.412 

143.14 

182.25 

2460.375 

3.6742 

2.3811 

13-6 

42.726 

145.27 

184.0 

2515.456 

3.6878 

2.3870 

13-7 

43.040 

147.41 

187.69 

257L353 

3.7013 

2.3928 

13-8 

43-?54 

149-57 

190.44 

2628.072 

3.7148 

2  .  3986 

13.9 

43.668 

I5L75 

193.21 

2685.619 

3.7283 

2.4044 

14.0 

43.982 

153.94 

196.00 

2744.000 

3.7417 

2.4IOI 

14.1 

44.296 

156.15 

I98.8I 

2803.221 

3.7550 

2.4I59- 

14.2 

44-611 

158.37 

201.64 

2863.288 

3.7683 

2.4216 

14-3 
14.4 

44-925 
45.239 

160.61 
162.86 

204.49 
2O7.36 

2924.207 
2985.984 

3-7*15 
3-7947 

2.4272 
2.4329 

14-5 

45-553 

165.13 

210.25 

3048.625 

3.8079 

2.4385 

14.6 

45.867 

167.42 

2I3.I6 

3II2.I36 

3.8210 

2.4441 

14.7 

46.181 

169.72 

216.09 

3176.523 

3.8341 

2.4497 

14.8 

46.496 

172.03 

219.04 

3241.792 

3.8471 

2.4552 

14.9 

46.810 

174-37 

222.01 

3307.949 

3.8600 

2.4607 

15-0 

47.124 

176.72 

225.00 

3375.000 

3-8730 

2.4662 

I5-I 

47.438 

179-08 

228.01 

3442.951 

3.8859 

2.4717 

15.2 

47-752 

181.46 

231.04 

35H.8o8 

3.8987 

2.4772 

15-3 

48.066 

183.85 

234.09 

3581.577 

3-9IJ5 

2.4825 

15-4 

48.381 

186.27 

237.16 

3652.264 

3.9243 

2.4879 

15.5 

48.695 

188.69 

240.25 

3723.875 

3.9370 

2.4933 

15.6 

49.009 

191.13 

243.36 

3796.416 

3.9497 

2.4986 

15-7 

49.323 

193.59 

246.49 

3869.893 

3-9623 

2  •  5039 

15-8 

49'637 

196.07 

249.64 

3944.312 

3-9749 

2.5092 

15-9 

49-951 

198.56 

252.81 

4019.679 

3.9875 

2.5146 

16.0 

50.265 

201.06 

256.00 

4096.000 

4.0000 

2.5198 

16.1 

50.580 

203.58 

259-21 

4173.281 

4-0125 

2.5251 

16.2 

50.894 

206.12 

262.44 

425L528 

4.0249 

2.5303 

16.3 

51.208 

208.67 

265.69 

4330-747 

4.0373 

2.5355 

16.4 

51-522 

211.24 

268.96 

4410.944 

4.0497 

2.5406 

16.5 

51.836 

213.83 

272.25 

4492.125 

4.0620 

2.5458 

16.6 

52.150 

216.42 

275.56 

4574.296 

4-0743 

2.5509 

16.7 

52.465 

219.04 

278.89 

4657.463 

4.0866 

2.5561 

16.8 

52.779 

221.67 

282.24 

4741.632 

4.0988 

2.5612 

16.9 

53.093 

224.32 

285.61 

4826.809 

4.1110 

2.5663 

17.0 

53.407 

226  98 

289.00 

49I3.000 

4.1231 

2.5713 

17.1 

53.721 

229.66 

292.41 

5000.211 

4.1352 

2.5763 

17.2 

54.035 

132.35 

295.84 

5088.448 

4.M73 

2.5813 

17-3 

54.350 

235-06 

299.29 

5177.717 

4-1593 

2.5863 

17.4 

54-664 

237.79 

302.76 

5268.024 

4-I7I3 

2.59J3 

8 


HANDY  TABLES, 
CONSTANTS — Continued. 


n 

Wir 

**4 

*« 

«« 

v; 

fc 

17-5 

54-978 

240.53 

306.25 

5359-375 

4.1833 

2.5963 

17-6 

55.292 

243.29 

309.76 

545L776 

4.1952 

2.6012 

17.7 

55.606 

246.06 

313.29 

5545.233 

4.2071 

2.6061 

17.8 

55.920 

248.85 

316.84 

5639.752 

4.2190 

2.6109 

17.9 

56.235 

251.65 

320.41 

5735-339 

4.2308 

2.6158 

18.0 

56.549 

254-47 

324.00 

5832.000 

4.2426 

2.6207 

18.1 

56.863 

257.30 

327-61 

5929.741 

4-2544 

2.6256 

18.2 

57.177 

260.16 

331.24 

6028.568 

4.2661 

2.6304 

18.3 

57.491 

263.02 

334.89 

6128.487 

4.2778 

2.6352 

18.4 

57.805 

265.90 

338.56 

6229.504 

4.2895 

2.6401 

18.5 

58.119 

268.80 

342.25 

6331.625 

4.3012 

2.6448 

18.6 

58.434 

271.72 

345.96 

6434.856 

4.3128 

2.6495 

18.7 

58.748 

274.65 

349.69 

6539.203 

4.3243 

2-6543 

18.8 

59.062 

277-59 

353-44 

6644  .  672 

4.3359 

2.6590 

18.9 

59.376 

280.55 

357-21 

6751.269 

4.3474 

2.6637 

19.0 

59-690 

283.53 

361.00 

6859.000 

4-3589 

2.6684 

19-1 

60.004 

286.52 

364.81 

6967.871 

4.3703 

2.6731 

19.2 

60.319 

289.53 

368.64 

7077.888 

4.3818 

2.6777 

19-3 

60.633 

292.55 

372.49 

7189.057 

4-3932 

2.6824 

19.4 

60.947 

295.59 

376.36 

730L384 

4.4045 

2.6869 

19-5 

6l.26l 

298.65 

380.25 

74I4.875 

4-4159 

2.6916 

19.6 

61.575 

301.72 

384-16 

7529.536 

4.4272 

2  .  6962 

19-7 

61.889 

304.81 

388.09 

7645.373 

4.4385 

2.7008 

19.8 

62  .  204 

307.91 

392-04 

7762.392 

4.4497 

2.7053 

19-9 

62.518 

3H.03 

396.01 

7880.599 

4.4609 

2.7098 

20.0 

62.832 

314.16 

400.00 

SOOO.OOO 

4.4721 

2.7144 

20.1 

63.146 

317.31 

404.01 

8120.601 

4.4833 

2.7189 

20.2 

63.460 

320.47 

408.04 

8242.408 

4.4944 

2.7234 

20.3 

63.774 

323  .  66 

412.09 

8365.427 

4-5055 

2.7279 

20.4 

64.088 

326  85 

416.16 

8489.664 

4-5166 

2.7324 

20.5 

64.403 

330.06 

420.25 

8615.125 

4.5277 

2.7368 

20.6 

64.717 

333-29 

424.36 

874I.8I6 

4.5387 

2.7413 

20.7 

65.031 

336.54 

428.49 

8869.743 

4-5497 

2-7457 

20.8 

65.345 

339-8o 

432.64 

8989.912 

4-5607 

2.7502 

20.9 

05.659 

343.07 

436.81 

9129.329 

4.57I6 

2-7545 

21.  0 

65.973 

346.36 

441.00 

926I.OOO 

4.5826 

2.7589 

21.  1 

66.288 

349.67 

445.21 

9393.931 

4-5935 

2.7633 

21.2 

66.602 

352-99 

449.44 

9528.128 

4.6043 

2.7676 

21.3 

66.916 

356.33 

453.69 

9663.597 

4.6152 

2.7720 

21.4 

67.230 

359-68 

457-96 

9800.344 

4.6260 

2.7763 

21.5 

67.544 

363-05 

462.25 

9938.375 

4.6368 

2  .  7806 

21.6 

67.858 

366.44 

466.56 

10077.696 

4.6476 

2.7849 

21.7 

68.173 

369-84 

470.89 

I02I8.3I3 

4-6583 

2  .  7893 

HANDY    TABLES. 
CONSTANTS — Continued. 


n 

nit 

*'J 

«* 

«» 

*n 

fc 

21.8 

68.487 

373-25 

475-24 

10360.232 

4.6690 

2.7935 

21.9 

68.801 

376.69 

479.61 

10503.459 

4.6797 

2.7978 

22.0 

69.115 

380.13 

484.00 

10648.000 

4-6904 

2  .  8021 

22.1 

69.429 

383.60 

488.41 

10793.861 

4.70H 

2.8063 

22.2 

69.743 

387.08 

492.84 

10941.048 

4.7II7 

2.8105 

22-3 

70.058 

390.57 

497.29 

11089.567 

4.7223 

2.8147 

22.4 

70.372 

394.08 

501.76 

11239.424 

4.7329 

2.8189 

22.5 

70.686 

397-61 

506.25 

11390.625 

4.7434 

2.8231 

22.6 

71.000 

401.15 

510.76 

11543.176 

4.7539 

2.8273 

22.7 

71.314 

404-71 

515-29 

11697.083 

4.7644 

2.8314 

22.8 

71.268 

408.28 

519.84 

11852.352 

4-7749 

2.8356 

22.9 

71.942 

411.87 

524.41 

12008.989 

4.7854 

2.8397 

23-0 

72.257 

415.48 

529-00 

12167.000 

4.7958 

2.8438 

23.1 

72.571 

419.  10 

533-6i 

12326.391 

4.8062 

2  •  8479 

23.2 

72.885 

422.73 

538.24 

12487.168 

4.8166 

2.8521 

23-3 

73.199 

426.39 

542.89 

12649.337 

4.8270 

2.8562 

23-4 

73.513 

430.05 

547.56 

12812.904 

4-8373 

2.8603 

23-5 

73.827 

433-74 

552.25 

12977.875 

4.8477 

2.8643 

23-6 

74.142 

437-44 

556.96 

13144.256 

4.8580 

2.8684 

23-7 

74.456 

44LI5 

561.69 

13312.053 

4.8683 

2.8724 

23-8 

74-770 

444.88 

566.44 

13481.272 

4.8785 

2.8765 

23-9 

75.084 

448.63 

571.21 

13651.919 

4.8888 

2.8805 

24.0 

75.398 

452-39 

576-00 

13824.000 

4.8990 

2.8845 

24.1 

75.712 

456.17 

580.81 

13997.521 

4.9092 

2.8885 

24.2 

76.027 

459.96 

585.64 

14172.488 

4-9I93 

2.8925 

24-3 

76.341 

463.77 

590.49 

14348.907 

4.9295 

2.8965 

24.4 

76.655 

467.60 

595.36 

14526.784 

4.9396 

2.9004 

24-5 

76.969 

471.44 

600.25 

14706.125 

4-9497 

2.Q044 

24.6 

77.283 

475.29 

605.16 

14886.936 

4.9598 

2-9083 

24.7 

77-597 

479.16 

610.09 

15069.223 

4-9699 

2.9123 

24.8 

77-9" 

483-05 

615.04 

15252.992 

4-9799 

2.9162 

24.9 

78.226 

486.96 

620.01 

15438.249 

4.9899 

2.92OI 

25.0 

78.540 

490.87 

625.00 

15625.000 

5.0000 

2.9241 

25.1 

78.854 

494.81 

630.01 

15813.251 

5-0099 

2.9279 

25.2 

79.168 

498.76 

635.04 

16003.008 

5-0199 

2.9318 

25-3 

79.482 

502.73 

640.09 

16194.277 

5-0299 

2.9356 

25-4 

79.796 

506.71 

645.16 

16387.064 

5-0398 

2-9395 

25-5 

80.  in 

510.71 

650.25 

16581.375 

5.0497 

2.9434 

25-6 

80.425 

5I4.72 

655-36 

16777.216 

5.0596 

2.9472 

25-7 

80.739 

518.75 

660.49 

16974.593 

5.0695 

2.9510 

25-8 

81.053 

522.79 

665.64 

I7I73-512 

5-0793 

2-9549 

25-9 

81.367 

526.85 

670.81 

17373-979 

5.0892 

2.9586 

10 


HANDY   TABLES. 
CONSTANTS —  Continued. 


n 

nit 

*'! 

it* 

«» 

*« 

h 

26.0 

8  1.  68  1 

530.93 

676.00 

17576.000 

5.0990 

2  .  9624 

26.1 

81.996 

535-02 

681.21 

17779-581 

5.1088 

2.9662 

26.2 

82.310 

539-13 

686.44 

17984.728 

5-1185 

2.9701 

26.3 

82.624 

543.25 

691.69 

18191.447 

5.1283 

2.9738 

26.4 

82.938 

547-39 

696.96 

18399.744 

5.1380 

2.9776 

26.5 

83.252 

55L55 

702.25 

18609.625 

5.1478 

2.9814 

26.6 

83.566 

555.72 

707.56 

18821.096 

5-1575 

2.9851 

26.7 

83.881 

559.90 

712.89 

19034-163 

5.1672 

2.9888 

26.8 

84.195 

564.10 

718.24 

19248.832 

f.i768 

2  .  9926 

26.9 

84.509 

568.32 

723.61 

19465.109 

5.1865 

2.9963- 

27.0 

84.823 

572.56 

729.00 

19683.000 

5.1962 

3.0000 

27.1 

85-I37 

576.8o 

734.41 

19902.511 

5-2057 

3-0037 

27.2 

85-451 

581.07 

739-84 

20123.648 

5.2153 

3.0074 

27-3 

85.765 

585.35 

745.29 

20346.417 

5.2249 

3.0III 

27.4 

86.080 

589.65 

750.76 

20570.824 

5-2345 

3-0147 

27-5 

86.394 

593  •  96 

756.25 

20796.875 

5.2440 

3.0184 

27.6 

86.708 

598.29 

761.76 

21024.576 

5-2535 

3-0221 

27-7 

87.022 

602  .  63 

767.29 

21253.933 

5-2630 

3-0257 

27.8 

87-336 

606.99 

772.84 

21484.952 

5-2725 

3.0293 

27.9 

87.650 

611.36 

778.41 

21717.639 

5.2820 

3.0330 

28.0 

87.965 

615.75 

784.00 

21952.000 

5-2915 

3.0366 

28.1 

88.279 

620.16 

789.61 

22188.041 

5-3009 

3  •  0402 

28.2 

88.593 

624.58 

795-24 

2242;..  768 

5-3103 

3-0438 

28.3 

88.907 

629.02 

800.89 

22  65.187 

5.3197 

3-0474 

28.4 

89.221 

633.47 

806.56 

22906.304 

5.3291 

3-0510 

28.5 

89.535 

637.94 

812.25 

23149.125 

5.3385 

3.0546 

28.6 

89.850 

642  .  42 

817.96 

23393.656 

5.3478 

3-0581 

28.7 

90.  164 

646.93 

823.69 

23639.903 

5-3572 

3-0617 

28.8 

90.478 

651.44 

829.44 

23887.872 

5-3665 

3-0652 

28.9 

90.792 

655.97 

835.21 

24137.569 

5.3758 

3.0688 

29.0 

91.106* 

660.52 

841.00 

24389.000 

5.3852 

3-0723 

29.1 

91.420 

665.08 

846.81 

24642.171 

5-3944 

3.0758 

29.2 

91-735 

669.66 

852.64 

24897.088 

5-4037 

3-0794 

29-3 

92.049 

674.26 

858.49 

25153.757 

5.4129 

3.0829 

29.4 

92.363 

678.87 

864.36 

25412.184 

5-4221 

3.0864 

29  5 

92.677 

683.49 

870.25 

25672.375 

5.4313 

3.0899 

29.6 

92.991 

688.13 

876.16 

25934.336 

5.4405 

3.0934 

29.7 

93.305 

692  .  79 

882.09 

26198.073 

5-4497 

3.0968 

29.8 

93-619 

697.47 

888.04 

26463.592 

5-4589 

3.1003 

29.9 

93-934 

702.15 

894.01 

26730.899 

5.4680 

3-1038 

30.0 

94.248 

706.86 

900.00 

27000.000 

5.4772 

3.1072 

30.1 

94-562 

711.58 

906.01 

27270.901 

5.4863 

3-1107 

30.2 

94.876 

716.32 

912.04 

27543.608 

5-4954 

3.1141 

HANDY  TABLES. 
CONSTANTS — Continued. 


II 


• 

nit 

"'I 

»a 

n* 

*n 

fc 

30.3 

95.190 

721.07 

918.09 

278  r8.  i  27 

5  •  5045 

3.1176 

30.4 

95  •  505 

725-83 

924.16 

28094.464 

5.5136 

3.1210 

30.5 

95.819 

730.62 

930.25 

28372.625 

5.5226 

3-1244 

30.6 

96.133 

735-42 

936.36 

28652.616 

5.5317 

3.1278 

30.7 

96.447 

740.23 

942.49 

28934.443 

5.5407 

3.1312 

30.8 

96.761 

745.06 

948.64 

29218.112 

5.5497 

3-1346 

30.9 

97-075 

749.91 

954.81 

29503.629 

5.5587 

3.1380 

31.0 

97.339 

754-77 

961.00 

29701.000 

5-5678 

3.I4I4 

3I-I 

97.704 

759.65 

967.21 

30080.231 

5.5767 

3.1448 

31-2 

98.018 

764-54 

973-44 

30371.328 

5-5857 

3-1481 

31-3 

98.332 

769.45 

979-69 

30664.297 

5-5946 

3-I5I5 

31-4 

98.646 

774-37 

985.96 

30959.144 

5-6035 

3.1548 

31-5 

98.960 

779.31 

992.25 

31255-875 

5.6124 

3.1582 

31.6 

99-274 

784.27 

998-56 

31554.496 

5.6213 

3.1615 

31-7 

99.588 

789.24 

1004.89 

31855.013 

5.6302 

3  .  1648 

31.8 

99.903 

794-23 

1011.24 

32157.432 

5-6391 

3.1681 

31-9 

100.22 

799-23 

1017.61 

32461.759 

5.6480 

3.I7I5 

32.0 

100.53 

804.25 

1024.00 

32768.000 

5-6569 

3.1748 

32.1 

100.85 

809.28 

1030.41 

33076.161 

5.6656 

3.1781 

32.2 

101.16 

8i4.33 

1036.84 

33386.248 

5-6745 

3-1814 

32.3 

101.47 

819.40 

1043.29 

33698.267 

5-6833 

3-J847 

32.4 

101.79 

824.48 

1049.76 

34012.224 

5-6921 

3.1880 

32.5 

102.10 

829.58 

1056.25 

34328.125 

5-7008 

3-i9J3 

32.6 

102.42 

834-69 

1062.76 

34645.976 

5-7096 

3-1945 

32.7 

102-73 

839.82 

1069.29 

34965  -  783 

5.7i83 

3.I978 

32.8 

103.04 

844-96 

1075.84 

35287.552 

5.7271 

3.2010 

32.9 

103.36 

850.12 

1082.41 

35611.289 

5.7358 

3.2043 

33-0 

103.67 

855.30 

1089.00 

35937.000 

5.7446 

3.2075 

33-1 

103.99 

860.49 

1095.61 

36264.691 

5.7532 

3.2108 

33-2 

104.30 

865.70 

1102.24 

36594.368 

5.7619 

3.2140 

33-3 

IO4.62 

870.92 

1108.89 

36926.037 

5.7706 

3.2172 

33-4 

104.93 

876.16 

1115.56 

37259.704 

5.7792 

3  .  2204 

33-5 

105.24 

881.41 

1122.25 

37595.375 

5.7879 

3-2237 

33-6 

105.56 

886.68 

1128.96 

37933.056 

5.7965 

3.2269 

33-7 

105.87 

891.97 

"35-69 

38272.753 

5-8051 

3.2301 

33-8 

106.19 

897-27 

1142.44 

38614.472 

5.8137 

3-2332 

33-9 

106.50 

902.59 

1149.21 

38958.219 

5.8223 

3-2364 

34-0 

106.81 

907.92 

1156.00 

39304.000 

5.8310 

3-2396 

34-i 

107.13 

913.27 

1162.81 

39651.821 

5.8395 

3-2428 

34-2 

107.44 

918.63 

1169.64 

40001.688 

5  .  8480 

3.2460 

34-3 

107.76 

924.01 

1176.49 

40353-607 

5.8566 

3-2491 

34-4 

108.07 

929.41 

1183.36 

40707.584 

5.8651 

3-2522 

12 


HANDY   TABLES. 
CONSTANTS — Continued. 


n 

nir 

«*? 
4 

«» 

n> 

v» 

fa 

34.5 

108.38 

934.82 

1190.25 

41063.625 

5-8736 

3-2554 

34-6 

108.70 

940.25 

1197.16 

41421.736 

5.8821 

3.2586 

34-7 

IOQ.OI 

945.69 

1204.09 

41781.923 

5.8906 

3-2617 

34-8 

109.33 

951.15 

1211.04 

42144.192 

5.8991 

3  .  2648 

34-9 

109.64 

956.62 

I2I8.0I 

42508.549 

5.9076 

3.2679 

35-0 

109.96 

962.11 

1225.00 

42875.000 

5.9161 

3.2710 

35-1 

110.27 

967.62 

I232.OI 

43243.551 

5.9245 

3.2742 

35-2 

110.58 

973.14 

1239.04 

43614.208 

5.9329 

3-2/73 

35-3 

IlO.gO 

978.68 

1246.09 

43986.977 

5.9413 

3.2804 

35-4 

III.  21 

984.23 

1253.16 

44361.864 

5  •  9497 

3-2835 

35-5 

"I-  53 

989.80 

1260.25 

44738.875 

5.9581 

3.2866 

35-6 

111.84 

995.38 

1267.36 

45118.016 

5-9665 

3.2897 

35-7 

112.15 

1000.98 

1274.49 

45499.293 

5-9749 

3.2927 

35-8 

112.47 

1006  .  60 

1281.64 

45882.712 

5.9833 

3-2958 

35-9 

112.78 

1012.23 

I288.8I 

46268.279 

5.9916 

3.2989 

36.0 

113.10 

1017.88 

1296.00 

46656.000 

6.0000 

3.3019 

36.1 

113.41 

1023.54 

1303.21 

47045.881 

6.0083 

3-3050 

36.2 

113-73 

1029.22 

1310.44 

47437.928 

6.0166 

3-3080 

36.3 

114.04 

1034.91 

1317.69 

47832.147  - 

6.0249 

3.3HI 

36.4 

H4.35 

1040.62 

1324.96 

48228.544 

6.0332 

3.3I4I 

39-5 

114.67 

1046.35 

1332.25 

48627.125 

6.0415 

3.3I7I 

•?6.6 

114.98 

1052.09 

1339.56 

49027.896 

6.0497 

3  •  3202 

36  7 

II5-30 

1057.84 

1346.89 

49430.863 

6.0580 

3-3232 

36.8 

115.61 

1063.62 

1354.24 

49836.032 

6.0663 

3-3262 

36.9 

H5.92 

1069.41 

1361.61 

50243.409 

6.0745 

3.3292 

37-o 

116.24 

1075-21 

1369.00 

50653.000 

6.0827 

3.3322 

37-1 

II6-55 

1081.03 

1376.41 

51064.811 

6  .  0909 

3-3352 

37-2 

116.87 

1086.87 

1383.84 

51478.848 

6.0991 

3.3382 

37-3 

117.18 

1092  .  72 

1391.29 

51895.117 

6.1073 

3-3412 

37-4 

117.50 

1098.58 

1398.76 

52313.624 

6.1155 

3.3442 

37-5 

117.81 

1104.47 

1406.25 

52734.375 

6.1237 

3-3472 

37-6 

118.12 

III0.36 

1413.76 

53I57-376 

6.1318 

3.3501 

37-7 

118.44 

III6.28 

1421.29 

53582.633 

6  .  1400 

3-3531 

37-8 

H8..75 

1122.21 

1428.84 

54010.152 

6.1481 

3.3561 

37-9 

119.07 

1128.15 

1436.41 

54439-939 

6.1563 

3-3590 

38.0 

119.38 

II34." 

1444.00 

54872.000 

6.1644 

3.3620 

38.1 

119.69 

1140.09 

I45I.6I 

55306.341 

6.1725 

3.3649 

38.2 

120.01 

1146.08 

1459.24 

55742.968 

6.1806 

3.3679 

38.3 

120.32 

1152.09 

1466.89 

56181.887 

6.1887 

3.3708 

38-4 

I2O.64 

1158.12 

1474.56 

56623.104 

6.1967 

3-3737 

38.5 

120.95 

1164.16 

1482.25 

57066.625 

6.2048 

3.3767 

38.6 

121.27 

1170.21 

1489.96 

57512.456 

6.2129 

3-3796 

38-7 

121.58 

1176.28 

1497.69 

57960.603 

6.2209 

3-3825 

HANDY  TABLES. 
CONSTANTS— Continued. 


* 

•r 

««? 

4 

«' 

ft* 

«Q 

fc 

38.8 

121.89 

1182.37 

1505.44 

58411.072 

6.2289 

3.3854 

38.9 

122.21 

1188.47 

1513.21 

58863.869 

6.2370 

3-3883 

39-o 

122.52 

1194-59 

1521.00 

59319.000 

6.2450 

3.3912 

39-1 

122.84 

1200.72 

I528.8I 

59776.471 

6.2530 

3-3941 

39-2 

123.15 

1206.87 

1536.64 

60236.288 

6.2610 

3.3970 

39-3 

123.46 

1213.04 

1544-49 

60698.457 

6.2689 

3-3999 

39-4 

123.78 

1219.22 

1552.36 

61162.984 

6.2769 

3.4028 

39-5 

124.09 

1225.42 

1560.25 

61629.875 

6.2849 

3.4056 

39-6 

124.41 

1231.63 

1568.16 

62099.136 

6.2928 

3-4085 

39-7 

124.72 

1237.86 

1576.09 

62570.773 

6.3008 

3.4II4 

39-8 

125.04 

I244.IO 

I584.04 

63044.792 

6.3087 

3.4142 

39-9 

125-35 

1250.36 

1592.01 

63521.199 

6.3166 

3.4I7I 

40.0 

125.66 

1256.64 

I600.00 

64000.000 

6.3245 

3-4200 

40.1 

125.98 

1262.93 

1608.  oi 

64481.201 

6.3325 

3-4228 

40.2 

126.29 

1269.23 

I6l6.04 

64964  .  808 

6.3404 

3-4256 

40-3 

I26.6I 

1275.56 

1624.09 

65450.827 

6.3482 

3-4285 

40.4 

126.92 

1281.90 

I632.I6 

65939.264 

6.3561 

3.4313 

40.5 

127.23 

1288.25 

1640.25 

66430.125 

6.3639 

3-4341 

40.6 

127.55 

1294.62 

1648.36 

66923.416 

6.3718 

3.4370 

40.7 

127.86 

I3OI.OO 

1656.49 

67419.143 

6.3796 

3.4398 

40.8 

I28.I8 

1307.41 

1664.64 

67911.312 

6.3875 

3-4426 

40.9 

128.49 

1313.82 

1672.81 

68417.929 

6.3953 

3-4454 

41.0 

I28.8I 

1320.25 

1681.00 

68921.000 

6.4031 

3.4482 

41.1 

129.12 

1326.70 

1689.21 

69426.531 

6.4109 

3.4510 

41.2 

129.43 

1333.17 

1697.44 

69934.528 

6.4187 

3-4538 

4L3 

129.75 

1339.65 

1705.69 

70444.997 

6.4265 

3.4566 

41.4 

130.06 

1346.14 

1713.96 

70957.944 

6-4343 

3-4594 

41-5 

130.38 

1352.65 

1722.25 

71473.375 

6.4421 

3-4622 

41.6 

130.69 

I359.I8 

1730.56 

71991.296 

6.4498 

3.4650 

41.7 

131.00 

1365.72 

1738.89 

72511.713 

6.4575 

3-4677 

41.8 

I3L32 

1372.28 

1747.24 

73034.632 

6.4653 

3.4705 

41.9 

131.63 

1378.85 

I755.6I 

73560.059 

6.4730 

3-4733 

42.0 

I3L95 

1385.44 

1764.00 

74088.000 

6.4807 

3.4760 

42.1 

132.26 

1392.05 

1772.41 

74618.461 

6.4884 

3.4788 

42.2 

132.58 

1398.67 

1780.84 

75151-448 

6.4961 

3.4815 

42-3 

132.89 

1405.31 

1789.29 

75686.967 

6.5038 

3-4843 

42.4 

133-20 

1411.96 

1797.76 

76225.024 

6.5115 

3.4870 

42.5 
42.6 

133-52 
133.83 

1418.63 
1425.31 

1806.25 
1814.76 

76765.625 
77308.776 

6.5192 
6.5268 

3.4898 
3.4925 

42.7 

134.15 

1432.01 

1823.29 

77854.483 

6-5345 

3.4952 

42.8 

134.46 

1438.72 

1831.84 

78402.752 

6.5422 

3.4080 

42.9 

134-77 

1445-45 

1840.41 

78953.  5*9 

6.5498 

3-5007 

HANDY   TABLES. 

CONSTANTS — Continued. 


n 

nit 

"'4 

«» 

«3 

¥m 

h 

43-0 

I35-09 

1452.20 

1849.00 

79507.000 

6-5574 

3  •  5034 

43-i 

135-40 

1458.96 

1857.61 

80062.991 

6.5651 

3.5061 

43-2 

135.72 

1465.74 

1866.24 

80621.568 

6.5727 

3.5088 

43-3 

136.03 

1472.54 

1874.89 

8ll82.737 

6.5803 

3.5H5 

43-4 

136.35 

1479-34 

1883.56 

81746.504 

6.5879 

3-5H2 

43-5 

136.66 

1486.17 

1892.25 

82312.875 

6-5954 

3.5i69 

43-6 

136.97 

1493.01 

1900.96 

82881.856 

6.6030 

3.5*96 

43-7 

137.29 

1499.87 

1909.69 

83453.453 

6.6rc6 

3-5223 

43-8 

137.60 

1506.74 

1918.44 

84027.672 

6.6182 

3.5250  ; 

43-9 

137.92 

1513.63 

1927.21 

84604.519 

6.6257 

3.5277 

44.0 

138.23 

1520.53 

1936.00 

85I84.OOO 

6.6333 

3.5303 

44.1 

138.54 

1527.45 

I944.8I 

85766.121 

6  .  6408 

3-5330 

44.2 

138.86 

1534-39 

1953.64 

86350.888 

6.6483 

3-5357 

44-3 

I39.I7 

I54L34 

1962.49 

86938.307 

6.6558 

3.5384 

44-4 

139-49 

1548.30 

1971.36 

87528.384 

6.6633 

3-54*0 

44-5 

I39.80 

1555.28 

1980.25 

88I2I.I25 

6.6708 

3-5437 

44.6 

140.12 

1562.28 

1989.16 

88716.536 

6.6783 

3-5463 

44-7 

140.43 

1569.30 

1998.09 

89314.623 

6.6858 

3  •  549° 

44.8 

140.74 

1576.33 

2007.04 

89915.392 

6.6933 

3.55I6 

44-9 

141  .  06 

1583.37 

2OI6.OI 

90518.849 

6.7007 

3-5543 

45-0 

I4L37 

1590.43 

2025.00 

91125.000 

6.7082 

3.  .5569 

45-1 

141.69 

I597.5I 

2O34.OI 

91733.851 

6.7156 

3-5595 

45-2 

142.00 

1604.60 

2043.04 

92345.408 

6.7231 

3-5621 

45-3 

142.31 

I6II.7I 

2O52.O9 

92959.677 

6.7305 

3-5648 

45-4 

142.63 

1618.83 

2061  .  16 

93576.664 

6-7379 

3-5674 

45-5 

142.94 

1625.97 

2070.25 

94196.375 

6-7454 

3-5700 

45-6 

143.26 

1633.13 

2079.36 

948l8.8l6 

6.7528 

3-5726 

45-7 

143-57 

1640.30 

2088.49 

95443-993 

6  .  7602 

3-5752 

45-8 

143.88 

1647.48 

2097  .  64 

96071.912 

6.7676 

3-5778 

45-9 

144.20 

1654.68 

2106.81 

96702.579 

6-7749 

3-5805  . 

46.0 

144.51 

1661.90 

2116.00 

97336.000 

6.7823 

3-5830 

46.1 

144.83 

1669.14 

2125.21 

97972.181 

6.7897 

3-5856 

46.2 

145.14 

1676.39 

2134.44 

986II.I28 

6.7971 

3-5882 

46-3 

145.46 

1683.65 

2143-69 

99252.847 

6.8044 

3.5908 

46.4 

145.77 

1690.93 

2152.96 

99897.344 

6.8117 

3-5934 

46.5 

146.08 

1698.23 

2162.25 

100544.625 

6.8191 

3.5960 

46.6 

146.40 

I705.54 

2171.56 

101194.696 

6.8264 

3-5986 

46.7 

146.71 

1712.87 

2180.89 

101847.563 

6.8337 

3.6011 

46.8 

147.03 

1720.21 

2190.24 

102503.232 

6.8410 

3-6037 

46.9 

147-34 

1727.57 

2199.61 

I03I6I.709 

6.8484 

3.6063 

47.0 

I47.65 

1734.94 

2209.00 

103823.000 

6.8556 

3.6088 

47-1 

147-97 

1742.34 

2218.41 

IO4487.III 

6.8629 

3-6114 

47.2 

148.28 

1749.74 

2227.84 

105154.048   1   6.8702 

3-6139 

HANDY   TABLES. 
CONSTANTS — Continued. 


n 

nit 

"'4 

•> 

«» 

v« 

Vn 

47-3 

148.60 

I757.I6 

2237.29 

105823.817 

6-8775 

3-6165 

47-4 

148.91 

1764.60 

2246.76 

106496  .  424 

6.8847 

3-6190 

47-5 

149-23 

1772.05 

2256.25 

107171.875 

6.8920 

3.6216 

47-6 

149-54 

1779-52 

2265.76 

107850.176 

6.8993 

3.6241 

47-7 

149.85 

1787.01 

2275.29 

108531.333 

6.9065 

3-6267 

47.8 

150.17 

1794.51 

2284.84 

109215.352 

6.9137 

3.6292 

47  9 

150.48 

1802.03 

2294.41 

109902.239 

6.9209 

3.63I7 

48.0 

150.80 

1809.56 

2304.00 

110592.000 

6.9282 

3-6342 

48.1 

151.11 

1817.11 

2313.61 

111284.641 

6-9354 

3-6368 

48.2 

151.42 

1824.67 

2323-24 

111980.168 

6.9426 

3-6393 

48.3 

I5I-74 

1832.25 

2332.89 

112678.587 

6.9498 

3.6418 

48-4 

152.05 

1839.84 

2342.56 

"3379.904 

6.9570 

3.6443 

48-5 

152.37 

1847-45 

2352.25 

114084.125 

6  .  9642 

3  .  6468 

48.6 

152.68 

1855.08 

2361.96 

114791.256 

6.9714 

3.6493 

48.7 

153-°° 

1862.72 

2371.69 

115501.303 

6.9785 

3-6518 

48.8 

I53.3I 

1870.38 

2381.44 

116214.272 

6.9857 

3.6543 

48-9 

153.62 

1878.05 

2391.21 

116930.169 

6.9928 

3-6568 

49.0 

153-94 

1885.74 

2401.00 

117649.000 

7.0000 

3-6593 

49.1 

154.25 

1893.45 

2410.81 

118370.771 

7.0071 

3.6618 

49-2 

154-57 

1901.17 

2420.64 

119095.488 

7-0143 

3-6643 

49-3 

154-88 

1908.90 

2430.49 

119823.157 

7.0214 

3.6668 

49.4 

I55-I9 

1916.65 

2440.36 

120553.784 

7.0285 

3.6692 

49-5 

155-51 

1924.42 

2450.25 

121287.375 

7-0356 

3-6717 

t* 

49.6 

155.82 

1932.21 

2460.16 

122023.936 

7.0427 

3-6742 

49-7 

156.14 

1940.00 

2470.09 

122763.473 

7  .  0498 

3-6/67 

49-8 

156.45 

1947.82 

2480.04 

123505.992 

7.0569 

3-6791 

49-9 

156.77 

1955.65 

2490.01 

124251.499 

7.0640 

3.6816 

50.0 

157-08 

1963.50 

2500.00 

125000.000 

7.0711 

3.6840 

51-0 

160.22 

2042  .  82 

2601.00 

132651.000 

7.1414 

3.7084 

52.0 

163.36 

2123.72 

2704.00 

140608.000 

7.2111 

3.7325 

53-0 

166.50 

2206.19 

2809.00 

148877:000 

7.2801 

3-7563 

54-0 

169.64 

2290.22 

2916.00 

157464.000 

7.3485 

3.7798 

55-0 

172.78 

2375.83 

3025.00 

166375.000 

7.4162 

3  •  8030 

56.0 

175  93 

2463.01 

3136.00 

175616.000 

7.4833 

3-8259 

57-o 

179.07 

2551.76 

3249-00 

185193.000 

7.5498 

3.8485 

58.0 

182.21 

2642.08 

3364.00 

195112.000 

7-6158 

3.8709 

59-0 

185.35 

2733-  ~7 

3481.00 

205379.000 

7.6811 

3.8930 

60.0 

188.49 

2827.44 

3600.00 

216000.000 

7.7460 

3-9M9 

61.0 

191.63 

2922.47 

3721.00 

226981.000 

7.8102 

3.9365 

62.0 

194-77 

3019.07 

3844-00 

238328.000 

7.8740 

3-9579 

63.0 

197.92 

3II7-25 

3969.00 

250047.000 

7.9373 

3-9791 

64.0 

201.06 

3216.99 

4096.00 

262144.000 

8.0000 

4.0000 

65-0 

204.20 

3318.31 

4225.00 

274625.000 

8.0623 

4.0207 

66.0 

207.34 

3421.20 

4356.00 

287496.000 

8.1240 

4-0412 

i6 


HANDY   TABLES. 
CONSTANTS — Continued. 


n 

nit 

** 

4 

«" 

«3 

Vn 

fa 

67.0 

210.48 

3525.66 

4489.00 

300763.000 

8.1854 

4-0615 

68.0 

213.63 

3631.69 

4624.00 

314432.000 

8.2462 

4.0817 

69.0 

216.77 

3739-29 

4761.00 

328509.000 

8.3066 

4.1016 

70.0 

219.91 

3848.46 

4900.00 

343000.000 

8.3666 

4.1213 

71.0 

223.05 

3959-20 

5041.00 

357911.000 

8.4261 

4.1408 

72.0 

226.19 

4071.51 

5184.00 

373248.000 

8.4853 

4  .  1602 

73-o 

229.33 

4185.39 

5329.00 

389017.000 

8.5440 

4-1793 

74.0 

232.47 

4300.85 

5476.00 

405224.000 

8.6023 

4.1983 

75-o 

235.62 

44I7.S7 

5625.00 

421875.000 

8  .  6603 

4.2172 

76.0 

238.76 

4536.47 

5776.00 

438976.000 

8.7178 

4-2358 

77.0 

241.90 

4656.63 

5929.00 

456533.000 

8.7750 

4-2543 

78.0 

245.04 

4773.37 

6084  .  oo 

474552.000 

8.8318 

4-2727 

79.0 

248.18 

49OI.68 

6241  .00 

493039.000 

8.8882 

4-2908 

80.0 

25L32 

5026.56 

6400.00 

512000.000 

8.9443 

4-3089 

81.0 

254-47 

5153.01 

6561.00 

531441.000 

9.0000 

4.3267 

82.0 

257.61 

5281.03 

6724.00 

551368.000 

9-0554 

4-3445 

83.0 

260.75 

5410.62 

6889.00 

571787.000 

9.1104 

4-3621 

84.0 

263  .  89 

554L78 

7056.00 

592704.000 

9.1652 

'4-3795 

85.0 

267.03 

5674.50 

7225.00 

614125.000 

9.2195 

4-3968 

86.0 

270.17 

58o8.8l 

7396.00 

636056.000 

9.2736 

4.4140 

87.0 

273.32 

5944.69 

7569.00 

658503.000 

9.3274 

4.4310 

8S.o 

276.46 

6082.13 

7744.00 

681472.000 

9.3808 

4.4480 

89.0 

279.60 

6221.13 

7921.00 

704969.000 

9.4340 

4.4647 

90.0 

282.74 

6361.74 

8100.00 

729000.000 

9.4868 

4.4814 

91.0 

285.88 

6503.89 

8281.00 

753571.000 

9-5394 

4-4979 

92.0 

289.02 

6647.62 

8464  .  oo 

778688.000 

9-5917 

4.5144 

93-0 

292.17 

6792.92 

8649  .  oo 

804357.000 

9.6437 

4.5307 

94.0 

295.31 

6939.78 

8836.00 

830584.000 

9-6954 

4-5468 

95-0 

298.45 

7088.23 

9025.00 

857375.000 

9.7468 

4-5629 

96.0 

301.59 

7238.24 

9216.00 

884736.000 

9.7980 

4-5789 

97.0 

304.73 

7389.83 

9409.00 

912673.000 

9.8489 

4-5947 

98.0 

307.87 

7542.98 

9604  .  oo 

941192.000 

9.8995 

4.6104 

99.0 

311.02 

7697.68 

9801.00 

970299.000 

9.9499 

4.6261 

100.  0 

3H.I6 

7854-00 

IOOOO.OO 

IOOOOOO.OOO 

10.0000 

4.6416 

HANDY   TABLES. 


It 

LOGARITHMS. 

HYPERBOLIC  LOGARITHMS. 


N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

.00 

0  0000 

•3° 

0.8329 

3-60 

.2809 

4.00 

.5892 

6.40 

-8563 

0.0488 

•35 

0-8544 

3-65 

•2947 

4-95 

•5994 

6.50 

.8718 

.10 

0.0953 

0.1398 

•40 
•45 

0-8755 
0.8961 

3-70 
3-75 

.3083 
•  3218 

S-oo 
5-05 

.6094 
.6194 

6.60 
6.70 

.8871 

.9021 

.20 

0.1823 

•5° 

0.9163 

•3350 

5.10 

.6292 

6.80 

.9169 

•  25 

0.2231 

0.9361 

3-85 

•  3481 

5-15 

.6390 

6.90 

•9315 

•30 

0.2624 

.60 

0-9555 

3-90 

•  3610 

5-20 

•6487 

7.00 

•9459 

•35 

0.3001 

•65 

0.9746 

3-95 

•3737 

5-25 

.6582 

7.20 

•9741 

40 

0.3365 

•70 

0-9933 

4.00 

•3863 

5-30 

.6677  i 

7.40 

.0015 

•45 

0.3716 

•75 

1.0116 

4-05 

.3987 

5-35 

.6771  i 

7.60 

.0281 

•5° 

0.4055 

.80 

1.0296 

4.10 

.4110 

5-4° 

.6864 

7.80 

.0541 

•55 

0.4383 

•85 

I-Q473 

4.15 

.4231 

5-45 

•  6956 

8.00 

.0794 

.60 

0.4700 

.90 

1.0647 

4.20 

•4351 

5-50 

.7047 

8.25 

.1102 

•65 

0.5008 

•95 

i.  0818 

4-25 

.4469 

5-55 

•7138 

8.50 

.  I4OI 

.70 

0.5306 

3-00 

1.0986 

4.30 

.4586 

5.60 

.7228 

8-75 

.1691 

•75 

0.5596 

3-°5 

I  .  ZI54 

4-35 

.4701 

5-65 

•7317 

9.00 

.1972 

.80 

0.5878 

1.1314 

4.40 

.4816 

5-7° 

•7405 

9-25 

.2246 

-85 

0.6152 

3-15 

1.1474 

4-45 

•4929 

5-75 

•  7492 

9-50 

•25^3 

.90 

•95 

0.6419 
0.6678 

3-20 

3-25 

1.1632 
1.1787 

4-50 

4-55 

.5041 
•5I5I 

5-8o 
5-85 

•7579 
.7664 

9-75 

IO.OO 

•2773 
.3020 

.00 

0.6931 

3-30 

"-1939 

4.60 

•  5261 

5-90 

•775° 

II.  OO 

•3979 

05 

0.7178 

3-35 

1.2000 

4.65 

•5369 

5-95 

.7834 

12.00 

.4849 

.10 

0.7419 

3-40 

1.2238 

4.70 

.5476 

6.00 

.7918 

13.00 

•5649 

•  15 

0.7655 

3-45 

1.2384 

4-75 

.558i 

6.10 

.8083 

14.00 

.6391 

.20 

0.7885 

3-50 

1.2528 

4.80 

.5686 

6.20 

•  8245 

15.00 

.7081 

•25 

0.8109 

3-55 

1.2669 

4-85 

•5790 

6.30 

.8405 

16.00 

.7726 

COMMON  LOGARITHMS:  10-1200. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

10 

00000 

00432 

00860 

01284 

01703 

02119 

02531 

02938 

03342 

03743 

396 

ii 

04139 

04532 

04922 

05308 

05690 

06070 

06446 

06819 

07188 

07555 

363 

12 

07918 

08279 

08636 

08991 

09342 

09691 

10037 

10380 

10721 

11059 

335 

J3 

"394 

11727 

12057 

"385 

12710 

13033 

13354 

13672 

13988 

14301 

312 

14 

14613 

14922 

15229 

15534 

15836 

16137 

16435 

16732 

17026 

17319 

290 

»S 

17609 

17898 

18184 

18469 

18752 

19033 

19312 

19590 

19866 

20140 

272 

16 

20412 

20683 

20952 

21219 

21484 

21748 

2201  1 

22272 

22531 

22789 

256 

17 

23045 

23300 

23553 

23805 

24055 

24304 

2455* 

24797 

25042 

25285 

242 

18 

»9 

25527 
27875 

25768 
28103 

26007 
28330 

26245 
28556 

26482 
28780 

26717 
29003 

26951 
29226 

27184 
29447 

27416 
29667 

27646 
29885 

229 
218 

20 

30103 

30320 

30535 

30750 

30963 

3"75 

31387 

3T597 

31806 

32015 

•07 

21 

32222 

32428 

32634 

32838 

33041 

33244 

33445 

33646 

33846 

34044 

198 

22 

34242 

34439 

34635 

34830 

35025 

35218 

354" 

35603 

35793 

35984 

189 

*4 

36173 
38021 

36361 
38202 

36549 
38382 

36736 
38561 

36922 
38739 

37107 
38917 

37291 
39094 

37475 
39270 

37658 
39445 

37840 
39620 

181 
174 

11 

39794 
4>497 

399«7 
41664 

40140 
41830 

40312 
41996 

40483 
42160 

40654 
42325 

40824 
42488 

40003 
42651 

41762 
42813 

41330 
42975 

167 
161 

11 

43*36 
44716 

43297 
44871 

43457 
45025 

43616 
45179 

43775 
4*332 

43933 
45484 

44091 
45637 

44248 
45788 

44404 
45939 

44560 
46090 

156- 
150 

SO 

46240 

46389 

46538 

46687 

46835 

46982 

47129 

47276 

47422 

47567 

1 

HANDY   TABLES. 
COMMON  LOGARITHMS — Continued. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

30 

477*2 

47857 

48001 

48144 

48287 

48430 

48572 

48714 

48855 

48996 

140 

3* 

49*36 

49276 

494*5 

49554 

49693 

4983* 

49969 

50106 

50243 

50379 

136 

32 

505*5 

5065* 

50786 

50920 

5*055 

5*188 

5*322 

5*455 

5*587 

5*720 

132 

33 

5*85* 

5*983 

52114 

52244 

52375 

52504 

52634 

52763 

52892 

53020 

128 

34 

53*48 

53275 

53403 

53529 

53656 

53782 

53908 

54033 

54*58 

54283 

124 

35 

54407 

54531 

54654 

54777 

54900 

55023 

55*45 

55267 

55388 

55509 

121 

36 

55630 

5575* 

5587* 

5599* 

56110 

56229 

56348 

56467 

56585 

56703 

**7 

37 

56820 

56937 

57054 

57287 

57403 

575*9 

57634 

57749 

57864 

**4 

38 

57978 

58092 

58206 

58320 

58433 

58546 

58659 

5877* 

58883 

58995 

in 

39 

59*o6 

59218 

59329 

59439 

5955° 

59660 

59770 

59879 

59988 

60097 

109 

40 

60206 

60314 

60423 

60531 

60638 

60746 

60853 

60959 

61066 

61172 

106 

41 

61278 

61384 

61490 

6i595 

61700 

61805 

61909 

62014 

62118 

62221 

104 

42 

62325 

62428 

62531 

62634 

62737 

62839 

62941 

63043 

63*44 

63246 

IOI 

43 

63347 

63448 

63548 

63649 

63749 

63849 

63949 

64048 

64*47 

64246 

99 

44 

64345 

64444 

64542 

64640 

64738 

64836 

64933 

65031 

65128 

65225 

97 

45 

65321 

654*8 

655*4 

65610 

65706 

65801 

65896 

65992 

66087 

66181 

95 

46 
47 

66276 
67210 

66370 
67302 

66464 
67394 

66558 
67486 

66652 
67578 

66745 
67669 

66839 
67761 

66932 
67852 

67025 
67943 

67117 
68034 

93 
90 

48 

68124 

68215 

68305 

68395 

68485 

68574 

68664 

68753 

68842 

68931 

89 

49 

69020 

69108 

69*97 

69285 

69373 

69461 

69548 

69636 

69723 

69810 

87 

50 

69897 

69984 

70070 

70*57 

70243 

70329 

7°4*5 

70501 

70586 

70672 

86 

5* 

70757 

70842 

70927 

71012 

71096 

71181 

7*265 

7*349 

7*433 

7*5*7 

84 

52 

71600 

71684 

71767 

71850 

7*933 

72016 

72099 

72181 

72263 

72346 

83 

53 

72428 

72509 

7259* 

72673 

72754 

72835 

72916 

72997 

73078 

73*59 

81 

54 

73239 

73320 

73400 

7348o 

7356o 

73640 

737*9 

73799 

73878 

73957 

80 

55 

74036 

74**  5 

74*94 

74273 

7435* 

74429 

74507 

74586 

74663 

74741 

78 

56 

748i9 

74896 

74974 

7505* 

75128 

75205 

75282 

75358 

75435 

755*1 

77 

75587 

75664 

75740 

75967 

76042 

76118 

76268 

76 

58 

76343 

76418 

76492 

76567 

76641 

76716 

76790 

76864 

76938 

77012 

74 

.59 

77085 

77*59 

77232 

773°5 

77379 

77452 

77525 

77597 

77670 

77743 

73 

60 

778i5 

77887 

77960 

78032 

78104 

78176 

78247 

783*9 

78390 

78462 

72 

78533 

78604 

78675 

78746 

78817 

78888 

78958 

79029 

79099 

79*69 

62 

79239 

79309 

79379 

79449 

795*8 

79588 

79657 

79727 

79796 

79865 

69 

63 

79934 

80003 

80072 

80140 

80209 

80277 

80346 

80414 

80482 

80550 

68 

•64 

80618 

80686 

80754 

80821 

80889 

80956 

81023 

81090 

81158 

81224 

67 

'65 

81291 

81358 

81425 

81491 

8*558 

81624 

81690 

8*757 

81823 

81889 

66 

'66 

8*954 

82020 

82086 

82151 

82217 

82282 

82347 

82413 

82478 

82543 

65 

167 

82607 

82672 

82737 

82802 

82866 

82930 

82995 

83059 

83*23 

83187 

64 

•69 

83251 
83885 

833*5 
83948 

83378 
84011 

83442 
84073 

83506 
84*36 

83569 
84198 

83632 
84261 

83696 
84323 

83759 
84386 

83822 
84448 

63 
63 

70 
7* 

84510 
85126 

84572 
85187 

84634 
85248 

84696 
85309 

84757 
85370 

84819 

8543* 

84880 
8549* 

84942 
85552 

85003 
85612 

85065 
85673 

62 
61 

72 

85733 

85794 

85854 

85974 

86034 

86094 

86153 

86213 

86273 

60 

73 

86332 

86392 

8645* 

86510 

86570 

86629 

86688 

86747 

86806 

86864 

59 

74 

86923 

86982 

87040 

87099 

87*57 

87216 

87274 

87332 

87390 

87448 

58 

75 

87506 

87^64 

87622 

87679 

87737 

87795 

87852 

87910 

87967 

88024 

58 

76 

88081 

88138 

88rg5 

88252 

88309 

88366 

88423 

88480 

88536 

88593 

57 

77 

88649 

88705 

88762 

88818 

88874 

88930 

88986 

89042 

89098 

89*54 

56 

78 

89209 

89265 

89321 

89376 

89432 

89487 

89542 

89597 

89653 

89708 

55 

79 

89763 

89818 

89873 

89927 

89982 

90037 

90091 

90146 

90200 

90255 

55 

80 

90309 

90363 

90417 

90472 

90526 

90580 

90634 

90687 

00741 

90795 

54 

81 

90849 

90002 

90956 

91009 

91062 

91116 

91169 

91222 

91275 

9*328 

53 

82 

91381 

9*434 

9*487 

9*540 

9*593 

9*645 

91698 

9*75* 

9*803 

9*855 

52 

83 

91908 

91960 

92012 

92065 

92117 

92169 

92221 

92273 

92324 

92376 

52 

84 

92428 

92480 

9253* 

92583 

92634 

92686 

92737 

92788 

92840 

92891 

85 

92942 

92993 

93°44 

93095 

93*46 

93*97 

93247 

93298 

93349 

93399 

5' 

86 

93450 

93500 

9355* 

93601 

9365* 

93702 

93752 

93802   93852 

93902 

50 

87 

93952 

94002 

94052 

94101 

94*5* 

94201 

94250 

94300  |  94349 

94399 

50 

HANDY   TABLES. 


COMMON  LOGARITHMS— Continued. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9   Diff. 

88 
89 

94448 
94939 

94498 
94988 

94547 
95036 

94596 
95085 

94645 
95134 

94694 
95182 

94743 
95231 

94792 
95279 

94841 
95328 

94890  |  49 
95376   49 

90 

95424 

95472 

95521 

95569 

95617 

95665 

95713 

9576i 

95809 

95856   48 

9' 
92 

95904 
96379 

KS 

95999 
96473 

96047 
96520 

96095 
96567 

96142 
96614 

96190 
96661 

96237 
96708 

96284 
96755 

96332 
96802 

47 
47 

93 

96848 

96895 

96942 

96988 

97035 

97081 

97128 

97  '74 

97220 

97267 

46 

94 

97313 

97359 

97405 

9745i 

97497 

97543 

97589 

97635 

97681 

97727 

46 

It 

97772 
98227 

97818 
98272 

97864 
98318 

979*9 

97955 
98408 

98000 
98453 

98046 
98498 

98091 
98543 

98137 
98588 

98182 
98632 

45 
45 

97 

98677 

98722 

98767 

98811 

98856 

98900 

98945 

98989 

99034 

99078 

45 

98 

99123 

99167 

99211 

99255 

99300 

99344 

99388 

99432 

99476 

99520 

44 

99 

99564 

99607 

99651 

99695 

99739 

99782 

99826 

99870 

99913 

99957 

44 

too 

00000 

00045 

00087 

00130 

00173 

00217 

00260 

00303 

00346 

00389  1  43 

101 

00432 

00475 

00518 

00561 

00604 

00647 

00689 

00732 

o°775 

00817   43 

102 

00860 

00903 

00945 

00988 

01030 

01072 

01115 

01157 

01199 

01242 

42 

103 

01284 

01326 

01368 

01410 

01452 

01494 

01536 

01578 

01620 

01662 

42 

104 

01703 

oi745 

01787 

01828 

01870 

01912 

01953 

01995 

02036 

02078 

42 

3 

02119 
02531 

02160 
02572 

02202 
O26l2 

02243 
02653 

02284 
02694 

02325 
02735 

02366 
02776 

02407 
02816 

02449 
02857 

02490 
02898 

4i 
41 

107 

02938 

02979 

03019 

03060 

03100 

03141 

03181 

03222 

03262 

03302   41 

108 

03342 

03383 

03423 

03463 

03503 

03543 

03583 

03623 

03663 

03703   40 

109 

03743 

03782 

03822 

03862 

03902 

03941 

03981 

04021 

04060 

04100  1  40 

no 

04139 

04179 

04218 

04258 

04297 

04336 

04376 

04415 

04454 

04493 

39 

III 

04532 

04571 

04610 

04650 

04689 

04727 

04766 

04805 

04844 

04883 

39 

112 

04922 

04961 

04999 

05038 

05077 

05"5 

05154 

05192 

05231 

05269 

39 

"3 

05308 

05346 

05385 

05423 

05461 

05500 

OSSS8 

05576 

95614 

05652 

38 

114 

05690 

05729 

05767 

05805 

05843 

05881 

05918 

05956 

05994 

06032 

38 

"5 

116 

06070 
06446 

06108 
06483 

06145 
06521 

06183 
06558 

06221 
06595 

06258 
06633 

06296 
06670 

06333 
06707 

06371 
06744 

06408 
06781 

38 
37 

117 

06819 

06856 

06803 

06930 

06967 

07004 

07041 

07078 

07115 

07151 

37 

118 
119 

07188 
07555 

07225 
07591 

07628 

07298 
07664 

07335 
07700 

07372 
°7773 

07408 
07773 

07445 
07809 

07846 

07518 
07882 

11 

Base  of  Naperian  logarithms, 

Log.  e  =  Modulus  of  common  logarithms, 


«=  2. 7182818   0.4342945 

ft  =  o .  4342945  9 . 6377843  -  10. 


20 


HANDY   TABLES. 


III. 
MEAN   PRESSURES   FOR  VARIOUS   METHODS  OF  EXPANSION. 

Values  of  — .     Adiabatic  Expansion  of  Steam. 


Ratio  of 

Expansion. 

1 

3 

u 

PERCENTAGE  OF  STEAM  AND  VALUE  OF  «. 

100 

i-i35 

90 
1.125 

80 
1.115 

76 
i.  in 

70 
1.105 

60 
1.095 

so 
1.085 

100 

1-333 

2 

} 

.829 

.831 

•833 

•834 

•835 

.836 

.837 

.810 

*i 

i 

.785 

.787 

.788 

.789 

.790 

.791 

•  793 

•754 

*i 

t 

•744 

.746 

•  747 

.748 

•749 

.750 

•  75  * 

.714 

2f 

T4T 

.707 

.708 

.710 

.711 

.712 

.713 

.714 

•675 

3 

i 

.675 

.676 

.677 

.678 

.679 

.681 

.683 

•639 

3* 

A 

.644 

.645 

.647 

.648 

.649 

.650 

.652 

.606 

3i 

* 

.633 

•  635 

.636 

•637 

•639 

.641 

•643 

.600 

3* 

f 

.616 

.618 

.619 

.620 

.622 

.624 

.626 

•576 

3t 

& 

•591 

•  592 

•593 

•594 

•59b 

.596 

•598 

•552 

4 

i 

.567 

.568 

•570 

•572 

.573 

•574 

•  576 

.523 

4* 

f 

.525 

•  527 

.528 

•530 

•531 

•533 

•534 

.486 

5 

1 

.488 

.491 

•493 

•494 

.496 

.498 

.500 

•447 

Si 

T8T 

.458 

.460 

.462 

.463 

.465 

.467 

.470 

.417 

6 

1 

•432 

•434 

•435 

•437 

•439 

.441 

•443 

•390 

N 

T1F 

.409 

.410 

.411 

.413 

.415 

.417 

.420 

•369 

7 

1 

.387 

•39° 

.392 

•394 

.400 

•403 

.405 

•345 

8 

i 

•  355 

•356 

•  357 

-358 

.360 

.361 

•363 

.312 

10 

iV 

.298 

.300 

.302 

•303 

•  304 

•305 

.308 

.263 

20 

* 

.170 

•173 

•175 

.177 

.178 

.180 

.182 

.144 

50 

A 

.080 

.082 

.083 

.084 

.084 

.085 

.086 

.063 

100 

T^ff 

.044 

•045 

•045 

.046 

.046 

.047 

048 

•034 

HANDY   TABLES. 


21 


III.— (Continued.) 

MEAN   PRESSURES   FOR  VARIOUS   METHODS  OF  EXPANSION. 
Values  of  *—  for  Steam,  Air,  Gas,  and  Mixtures. 


—  ' 

§3 

§8 

Steam  and  Leak- 

S3 

Gases. 

iT 

"8  § 

? 
3 

1§- 

-:    _     — 

O   w 

U  ~ 
c  *T 

age,  Actual  En- 
gines 

If 

el 

Q 

g-J?  ? 

.*•  c 
u    »• 

gl&JVO. 

>  g 

II 

•3    MI'K 
£ 

a  -o   . 
6  S  s 

<o 

If 

Isother- 

Adiabat- 

N 

1 

2b 

WQ 

|l 

*,  0.50. 

*.  0.75. 

JJ 

mal,  w, 

1.  00. 

ic,  *, 
1.41. 

2 

* 

.841 

.825 

.914 

•  875 

.783 

.846 

.801 

2* 

* 

•793 

.787 

.888 

.844 

•733 

.804 

•753 

2i 

| 

.760 

•745 

.866 

.800 

•  683 

.765 

•707 

2i 

A 

•717 

.700 

.846 

•785 

.638 

•  731 

.668 

3 

i 

•695 

.665 

.824 

•752 

•598 

.699 

.638 

9* 

* 

•  665 

.635 

.802 

•732 

-578 

.670 

•596 

3i 

TV 

.652 

.625 

.796 

.716 

.568 

.661 

.588 

3i 

I 

.632 

•  605 

.782 

.704 

•    .548 

.642 

.568 

91 

A 

.608 

.580 

•  775 

.684 

•515 

.616 

•538 

4 

i 

.587 

•550 

•  750 

.664 

.486 

.566 

.518 

4* 

I 

•540 

.510 

.720 

.624 

.441 

•555 

•473 

5 

i 

.510 

.482 

•695 

.600 

.406 

.522 

.428 

Si 

A 

.478 

•455 

•  674 

.560 

-371 

.492 

.406 

6 

i 

•454 

.420 

•  650 

•530 

•349 

•465 

•378 

6| 

A 

•430 

•39° 

.632 

•  515 

.326 

.441 

•358 

7 

} 

.409 

•375 

.612 

•  500 

•303 

.421 

•337 

8 

i 

•372 

•340 

.697 

.468 

.276 

.385 

.302 

10 

A 

•  326 

.284 

•532 

.412 

.225 

•330 

253 

20 

A 

.192 

.165 

.396 

.272 

.103 

.200 

.138 

50 

& 

.091 

.074 

.245 

•193 

.050 

.098 

.060 

100 

* 

.053 

.040 

.180 

•  134 

•  025 

.056 

•  032 

22 


HANDY   TABLES. 


I II. — (Continued!) 
MEAN   PRESSURE  RATIOS. 


r 

A 

B 

C 

r 

A 

B 

C 

r 

A 

B 

C 

r 

A 

B 

C 

.0 

I.OOO 

I.OOO 

I.OOO 

5-3 

.478 

•  5°3 

.488 

9.6 

.312 

.340 

•324 

7.8 

.194 

.218 

.204 

.1 

0.996 

0.996 

0.996 

5-4 

.472 

•  497 

.482 

9-7 

.310 

.338 

.322 

8.0 

.192 

.216 

.202 

.2 

0.983 

0.983 

0.983 

5-5 

.467 

.492 

•477 

9.8 

•  3°7 

•335 

•3*9 

8.2 

.190 

.215 

.2OO 

•  3 

.966 

.968 

.967 

5-6 

.461 

.486 

•  471 

9-9 

•  305 

•333 

•317 

8.4 

.189 

.214 

.199 

•  4 

•  947 

•952 

•950 

5-7 

•  456 

.481 

.466 

IO.O 

•  3°3 

•330 

•  3M 

8.6 

.187 

.212 

.197 

•  5 

.928 

•934 

•931 

5-8 

•45° 

•475 

.460 

IO.2 

.299 

•  325 

.310 

8.8 

.185 

.210 

195 

.6 

.910 

.919 

.914 

5-9 

•445 

.47° 

•455 

10.4 

•  295 

.321 

19.0 

.183 

.208 

•193 

•  7 

.890 

.900 

•  895 

6.0 

.440 

•  465 

•450 

10.6 

.291 

•3X7 

.302 

19.2 

.182 

.207 

.192 

.8 

.870 

.880 

•875 

6.1 

•  434 

.460 

•445 

10.8 

.287 

•3I3 

.298 

19.4 

.180 

.205 

-igO 

•9 

.850 

.862 

.856 

6.2 

•429 

•455 

.440 

II.  0 

.283 

•3°9 

.294 

19.6 

.179 

.204 

.189 

.0 

.833 

.846 

.840 

6-3 

•  424 

•  450 

•435 

II.  2 

.279 

•3°5 

.290 

19.8 

.178 

.202 

.l87 

.1 

.817 

.830 

.824 

6-4 

.419 

•  445 

•43« 

II.4 

•  275 

.301 

.286 

20.  o 

.177 

.2OO 

.186 

.2 

.798 

.812 

.805 

6-5 

.414 

.441 

.426 

ii.  6 

.272 

.298 

•  283 

2O.  2 

•175 

.198 

.I84 

•  3 

.780 

•795 

.787 

6.6 

.409 

•436 

.421 

n.  8 

.268 

•294 

.279 

20.4 

.174 

.196 

.183 

•4 

•763 

.780 

.771 

6.7 

•  4°5 

•432 

.417 

12.0 

.264 

.290 

•275 

20.  6 

•173 

.194 

.182 

•  5 

.748 

.766 

.756 

6.8 

.4101 

.428 

12.2 

.26t 

.287 

.272 

20.8 

.171 

•193 

.ISO 

.6 

•732 

•750 

.740 

6.9 

•396 

.424 

'lei 

12.4 

•257 

.283 

.268 

21.  0 

.192 

.178 

•  7 
.8 

.718 

.736 

.726 

7.0 

•393 

.421 

.405 

12.6 

•  254 

.280 

.265 

.262 

21.2 

.168 

.191 

.177 

T7& 

•9 

•7°5 
.692 

.710 

.700 

7-2 

•385 

•413 

•397 

I3.0 

.248 

.277 

.274 

•259 

21  .  4 
21.6 

.'165 

.  IQO 

.188 

.  I7O 
.174 

3-° 

.680 

.699 

.688 

7-3 

.381 

.410 

•393 

13.2 

•  245 

.271 

.256 

21.8 

.164 

.187 

•173 

3-1 

.668 

.687 

.676 

7-4 

•377 

.406 

13-4 

.242 

.268 

•253 

22.0 

.163 

.186 

.172 

S-2 

.656 

•675 

.664 

7-5 

•373 

.402 

.386 

I3.6 

•  239 

.265 

.250 

22.2 

.162 

.185 

.171 

3-3 

.645 

.664 

•  653 

7-6 

•370 

•399 

•383 

13-8 

.236 

.262 

.247 

22.4 

.161 

.i84 

.170 

3-4 

.634 

•653 

.642 

7-7 

•367 

.396 

.380 

14.0 

•  234 

.260 

•245 

22.6 

.160 

.183 

.169 

3-5 

.622 

.642 

.631 

7-8 

•363 

•392 

.376 

14.2 

.231 

•257 

.242 

22.8 

•J59 

.182 

.168 

3-6 

.612 

•632 

.621 

7-9 

.360 

•389 

•373 

14.4 

.228 

•254 

•239 

23.0 

.158 

.180 

.167 

3-7 

.602 

.622 

.611 

8.0 

.356 

•385 

•370 

I4.6 

.225 

.251 

•  236 

23-2 

.156 

.179 

.165 

3-8 

•593 

•  613 

.602 

8.1 

•353 

•  382 

•367 

I4.8 

.223 

.249 

•234 

23.4 

•155 

.178 

.I64 

3-9 

•584 

.604 

•593 

8.2 

•350 

•379 

•364 

15.0 

.221 

.247 

•  232 

23.6 

•154 

.177 

.163 

4.0 

•572 

.596 

•583 

8-3 

•347 

•376 

•  361 

15.2 

.219 

•  245 

.230 

23-8 

•153 

.176 

.162 

•565 

•587 

•575 

8.4 

•344 

•373 

•358 

15-4 

.217 

.242 

.227 

24.0 

.151 

.174 

.160 

4.2 

•556 

.578 

.566 

8-5 

•341 

•371 

•355 

15-6 

.215 

.240 

•  225 

24.2 

•  150 

•  173 

•159. 

4-3 

.548 

•57° 

•558 

8.6 

•338 

•  368 

•352 

15-8 

.21; 

.238 

.22 

24.4 

.149 

.172 

.158 

4-4 

•54° 

.563 

•550 

8.7 

•335 

•  364 

•349 

16.0 

.211 

.236 

.22 

24.6 

.148 

.171 

4-5 

•532 

•555 

•542 

8.8 

•332 

•  361 

•346 

16.2 

.209 

•234 

.219 

24.8 

.147 

.170 

•  156 

4-6 

•525 

•548 

•535 

8.9 

•33° 

•358 

•34 

16.4 

.207 

.232 

.217 

25.0 

.146 

.169 

•155 

4-7 

.518 

•542 

.528 

9.0 

•327 

•355 

•340 

16.6 

•  205 

.230 

.21 

4-8 

•5" 

•535 

.521 

9.1 

•324 

•353 

•337 

16.8 

.20; 

.228 

.21 

4-9 

.504 

.528 

•514 

9.2 

•  322 

•351 

•335 

17  o 

.201 

.226 

.21 

5-0 

.496 

.522 

•  506 

9-3 

•  320 

•348 

•332 

17.2 

.199 

.224 

.209 

5*  * 

.490 

•5*5 

.500 

9.4 

•  3*7 

•345 

•329 

17.4 

.197 

.222 

.207 

5-2 

.484 

•509 

•494 

9-5 

•315 

•343 

•327 

17.6 

•  195 

.220 

.205 

Column  r,  the  ratio  of  expansion  =  — 

»1 

"     A ,  ratio  of  mean  to  initial  pressure,  — 

P\ 


A, 


For  dry  steam,  expand- 
ed without  gain  or  loss 
of  heat,  in  a  non-con- 
ducting cylinder. 

i  +  hyp.  log.   r  (  For     damP     steam, 
J   expanded      receiv- 
ing heat. 

.  For    dry     steam,    ex- 
_  i&r — IB      ;    panded         receiving 
icat  sufficient  to  pre- 
vent liquefaction. 

RULE. — To  find  the  mean  pressure  exerted  throughout  the  stroke,  multiply  the  initial  pres- 
sure by  the  number  opposite  the  ratio  of  expansion,  in  the  column  corresponding  witn  the 
conditions  of  expansion.  (From  Northcott.) 


P.  log-    r   j  Fc 

1    " 
(Fa 

3  & 
1  h* 

(    ve 


HANDY   TABLES. 


IV. 

TERMINAL  PRESSURE  RATIOS 


pi 


r 

* 

B 

C 

r 

A 

B 

C 

r 

A 

B 

C 

r 

A 

B 

C 

.0 

0.00 

o.o 

o.oo 

4-7 

5-58 

4-7 

5-18 

8-3 

10.5 

8-3 

8  A 

9.47 

13.8 

l8.5 

18.8 

13.8 

16.2 

.2 

.33 

1.2 

.21 

4-9 

5-84 

4-9 

8-5 

10.7 

o  .  4 

9-59 
9-64 

14.0 
14.2 

19.1 

14.0 
14.2 

I*'.! 

•3 

•34 

'•3 

•32 

5.98 

5-52 

8.6 

10.9 

8.6 

9.76 

14-4 

19.4 

14-4 

17.0 

•  4 

•45 

x-4 

•43 

5-i 

6.  ii 

5-i 

5-64 

8-7 

II.  0 

8.7 

9.88 

i4.6 

19.7 

14.6 

17.2 

.5 
.6 

% 

1:1 

3 

5-2 

5-3 

6.24 
6.38 

5-2 

5-3 

5^88 

8.8 
8.9 

II.  2 

"•3 

8.8 
8.9 

10.0 
10.2 

14.8 
15-0 

20.  o 
20.3 

14.8 
15.0 

£i 

•7 

.80 

1-7 

•75 

5-4 

6-51 

5-4 

6.00 

9.0 

"•5 

9.0 

I0.3 

15-2 

20.6 

15-2 

18.0 

.8 

.92 

1.8 

.87 

5-5 

6.64 

6.12 

9.1 

ii.  6 

9.1 

10.4 

15-4 

20.9 

18.2 

«9 

• 

1.9 

.98 

5-6 

6.78 

5-6 

6.23 

9-2 

n.  8 

9-2 

10.6 

15.6 

21.2 

15.6 

18.5 

.0   .16 

2.O 

.08 

5.7 

6.91 

5-7 

6-35 

9-3 

11.9 

9-3 

10.7 

15.8 

21.5 

15  8 

18  7 

.1   .28 

2.1 

.20 

5-8 

7.05 

6.47 

9-4 

12.0 

9-4 

10.8 

16.0 

21.8 

16.0 

19.0 

.2    .40 

.3   -53 
•4   -64 

2.2 
2-3 
2-4 

•SI 

•42 

•53 

5-9 
6.0 
6.1 

7.18 
7-32 
7-45 

5-9 
6.0 
6.1 

6-59 
6.71 
6.83 

9-5 
9.6 
9-7 

12.2 
12.3 

9-5 
9.6 
9-7 

10.9 

II.  0 

ii.  i 

16.2 
16.4 
16.6 

22.1 
22.4 
22  7 

16.2 
16.4 
16.6 

19-3 
19.5 
19.8 

-5:   .76 

2-5 

•64 

6.2 

7-59 

6.2 

6.95 

9.8 

12.6 

9.8 

"•3 

16.8 

23.0 

14.8 

20.0 

.6 

2.6 

.76 

6-3 

7-73 

6-3 

7.07 

9-9 

12.8 

9-9 

11.4 

17.0 

23-3 

17.0 

20.3 

.7 

3-oi 

2.7 

.87 

6.4 

7.86 

6.4 

7.18 

IO.O 

12  9 

IO.O 

"•5 

17.2 

23-6 

17.2 

20.5 

•9 

3-  '4 
3.26 

2.8 

2.9 

•99 

.10 

6.5 
6.6 

8.00 
8.14 

6-5 
6.6 

7-30 
7.42 

10.2 
10-4 

13.2 
13-5 

IO.2 
10.4 

11.7 

12.0 

J7-4 
17.6 

23-9 
24.2 

'7-4 
17.6 

20.8 
21.0 

3-0 

3-39 

3.0 

.21 

6.7 

8.27 

6.7 

7-54 

10.6 

I3-8 

10.6 

12.3 

17.8 

24-5 

17.8 

21.3 

3-Si 

3-i 

•32 

6.8 

8.41 

6.8 

7  66 

10.8 

14.1 

10.8 

12-5 

18.0 

24.8 

18.0 

21.  0 

3-2 

3-64 

3-2 

:  -43 

6.9 

8-55 

6.9 

7.78 

II.  0 

II.  0 

12.8 

18.2 

25-1 

18.2 

21.8 

3-3 

3-77 

3-3 

7.0 

8.69 

7.0 

7.90 

II.  2 

14.6 

II.  2 

13-0 

18.4 

25-4 

18.4 

22.  0 

3-4 

3  -80 

3-4 

.67 

7-1 

8.83   7.1 

8.02 

II.4 

14.9 

ii..: 

13-3 

18.6 

25-7 

18.6 

22.3 

4.02 

3-5 

•79 

7-2 

8.96   7.2 

8.14 

ii.  6 

15.2 

ii.  6 

13-5 

18.8 

26.* 

18.8 

22.§ 

3-6 

4-15 

3-6 

.90 

7-3 

9.  10 

7-3 

8.27 

ii.  8 

iS-5 

ii.  8 

13-7 

19.0 

26.3 

19.0 

22.8 

3-7 

4.28 

3-7 

.01 

7-4 

9.24 

7-4 

8.38 

12.  0 

15  8 

12.0 

14.0 

19.2 

26.6 

19.2 

23-X 

3-8 
3-9 

4.41 

4-54 

3-8 
3-9 

•13 
•25 

J:i 

9-38 
9.52 

8-49 
8.62 

12.2 
12.4 

16.1 
16.4 

12.2 
12-4 

14.2 
14-5 

19.4 
19.6 

26.9 
27.3 

19.4 
19.6 

23.| 
23.6 

4.0 

4.66 

4.0 

.36 

7-7 

9.66 

7-7 

8.74 

12.6 

16.7 

12.6 

14.8 

19.8 

37.5 

19.8 

23-9 

4*  * 

4-79 

4'  * 

•47 

7-8 

9.80 

7-8 

8.87 

12.8 

17.0 

12.8 

15.0 

20.0 

27.9 

20.0 

24.  x 

4-2 

4.3 

4.91 
5-05 

4-2 

43 

.60 
•71 

7-9 
8.0 

9-94 

10.  I 

7-9 
8.0 

8-99 
9.11 

13-0 
13-2 

13.0 
13-* 

15.2 
15-5 

21,0 
22.  0 

29-5 
31-0 

21.0 
22.0 

25-4 
26.7 

4-4 

5-18 

4-4 

.82 

8.1  10.2 

8.1 

9-23 

13-4 

17.9 

13-4 

15-7 

23.0 

32.6 

23.0 

28.O 

J:I 

5.32 
5-45 

4-5 
4.6 

•95 
5-o6 

8.2 

10.3 

8.2 

9-35 

18.2 

13-6 

16.0 

24.0 

24.0 

29-3 

Column  r,  ratio  of  expansion  =  — 

"     A ,  ratio  of  initial  to  final  pressure,  /3 

"    B,         **          "          M  /, 

*•    c         **         **         M         **  p\ 


(  For  dry  steam,  expanded  with- 
•<  out  gain  or  loss  of  heat  in  a 
l  non-conducting  cylinder. 

j  For  damp  steam,  expanded 
J  receiving  heat. 

For  dry  steam,  expanded  re- 
ceiving sufficient  heat  to  pre- 
vent liquefaction. 

:.— To  find  the  final  pressure  obtaining  with  any  ratio  of  expansion,  divide  the  initial 
pressure  hv  'he  number  opposite  the  ratio  of  expansion,  in  the  column  corresponding  with  the 
"ition*  of  expansion. 


HANDY   TABLES. 


f 


1^      (jj       Q 


».  a 


jo 


J3liog 


•areais  jo  A"DU3pijj3 


•anon  jsd  j3A\od 
-SSJOH  pajBOipai 
jsd  pspusdxs  }B3]3 


niBSis  istmjxg  sqi 

m[M  JJO  P3U4BO  1B9H 


jo  -qj  jsd  ps^BOip 
-ui  J3MOJ  aApopf 


pspusd: 


jo  -qi 


uoisuBdxg  Sui 


jo  'qj  J3d  aap 


•jj  o££  jo  pasds  qjiAV. 

J3.\VOd-3SJOH  PW3 

ipu  j  J3d  B3jy  uoisi<j 


•anon 


g  jo 


-anoH 

J3d  J3MOd-3SJOH 


IB  sansssjj 


•aansssjd  IB:JOI  UBSJ^ 


•aoisaBdxg  jo  OIJB^ 


•ui  'bs  jsd  ajnsssjd 


'  ^^R 


NNC4NMM 


r^oo   t^  w  O 

W     M     H     100* 


OO  ^*-vo  t/>  t^  CO  ON  O^  cooo  O  vo  vo  CO  w  00 

t>  -4-00  M  -<J-oo  dci  Mcowt>.cod  tooo 

tovo  vo   tx  tx  t^oo  CO  cr»OH»MWrororo 


fa  2 


oooooooo     oooooooo 


o  o    oso>q\8.  0.3.0.0.     o  0    o>  ON  8r  q^  3  q  q_  q^ 
fe  H          H~  H~  H"  H"  H'  w"    fc  - 


\o  o^vo  ir>  -^-  ro  i 

1OM    O^t^lO^f 


vo  r>.  o  «•>  >*  N 

-1-  M    &VO    10  •*• 


O  O  I^OOOVO  txro 
HI  ITvo   fO  O  tx  10  <*• 

CO  N    H    M    M 


O  vo  r^  i-»oo  •<*•  ro  ro 
O  N  t^oo  oo  ro  re  ir> 
to  o  t^oo  oo  oo  iovo 
O  ro  covo  CMN  oo  >o 


oo  1 
i-    t^ 


10  o>  o  ^oo  tx  o> 

OMO  -<j-  N    M    O    O 

(NNNMCINM 


^Nint^O   N   -«f 
to  m  io\c  vo  ^o 


OOOOOOO 

vOoo   0   w   ioO   uS 

M  M  M  o)  w 


\OVOVOVO\OVOVOVO 


^^•^^•^•^^t-^  (N.VO  vo   10  O^  N   me 

^vo  00   O    rooo    c^OO  •     •      ... 


t>-vo  vo   to  O>  (N  tOOO 

O     tx-^HVO     O^M     CO 

tOVO  00    0    N  VO    M    10 


u  0 


HANDY   TABLES. 


°2^" o'oTSSSS  J2°««8*«"«5«'tf?3  e)***?*?** 

.-OIWttMMMHH  ***wMW>4»«l"iM*HH  r-^^KMHHMWHH 


Q.  q.  o  o  o  o  3  q. 


£8 


oooooooo 


MMNMCineici 


>o  o>  t^  cno> 

MAM  I^OO 
aMMMM 


|2wMM«M«MM          J^gMMMWWMWM          ^glHMMMMMMM 


£1 


wO   M\O   t^O    r^^f 

m  co  en0?  «  ?  S  5 


j  ef  J  cf  et  et  cf  S" 


oooooooooooaoooo 


ts.  o>  M  moo  c?\oo  o  MOOOOOOOCTOO  o»t«.q*o>«t«.'* 

in  6  oo\s  •*  <N  M  ~  >c  •<*•  e«  M  w  o  o>oo  MOO  o-oo  oo  tx  t^ 


§vo  ei  ^*-vc  vc  ^  -^  so  M  oo 

ininO«nm«o  «oof~ 

<>oo  «_  ^oo  in  «_  oo IK?  t 

tx  -»coo  M  ro  w  r~  o>  c 
t^  o  o  n  n->  mvo  t^ 


c. 

-  •*  -  r-. 


o  ^  •:«  - 


VCOOM  O«»"O>-'VOOOM 


0000    (•»«*•«    COWOO 

o>  6  «  ci  rn^ioin 


0     M     MNO     «>000     M 


t-iMCffnr^  m^o  t^ 


| 


M     M     M     CI     CI 


OO 

•2  oo 


tf   1  .1 

I    o|i 

1    til 

-5  X  3 


I 


26 


HANDY  TABLES. 


VI. 

COMPARISON  OF  THERMOMETERS. 


Celsius. 

Rdaumur. 

Fahren- 
heit. 

Celsius. 

Reaumur. 

Fahren- 
heit. 

Celsius. 

Reaumur. 

Fahren- 
heit. 

—  20 

-16 

-4 

25 

20.0 

77.0 

70 

56.0 

158.0 

—  19 

—  15-2 

—  2.2 

26 

20.8 

78.8 

71 

56.8 

159-8 

—  18 

-T4-4 

-0.4 

27 

21.6 

80.6 

72 

57.6 

161.6 

—  17 

-13.6 

1.4 

28 

22.4 

82.4 

73 

58.4 

163.4 

—  16 

-12.8 

3.2 

29 

23.2 

84.2 

74 

59.2 

165.2 

—15 

—  12.  0 

5-0 

30 

24.0 

86.0 

75 

60.0 

167.0 

—14 

—  II.  2 

6.8 

31 

24.8 

87.8 

76 

60.8 

168.8 

—13 

—  10.4 

8.6 

32 

25.6 

89.6 

77 

61.6 

170.6 

—  12 

-9.6 

10.4 

33 

26.4 

91.4 

78 

62.4 

172.4 

—II 

-8.8 

12.2 

34 

27.2 

93-2 

79 

63.2 

174.2 

—  IO 

-8.0 

14.0 

35 

28.0 

95-0 

80 

64.0 

176.0 

—9 

—7.2 

15-8 

36 

28.8 

96.8 

81 

64.8 

177.8 

—8 

-6.4 

I7.6 

37 

29.6 

98.6 

82 

65.6 

179.6 

—7 

-5-6 

19.4 

38 

30.4 

100.4 

83 

66.4 

181.4 

—6 

-4.8 

21.2 

39 

31.2 

IO2.2 

84 

67.2 

183.2 

—5 

—4.0 

23.0 

40 

32.0 

104.0 

85 

68.0 

185.0 

—4 

-3-2 

24.8 

41 

32.8 

105.8 

86 

68.8 

186.8 

-3 

-2.4 

26.6 

42 

33-6 

107.6 

87 

69.6 

188.6 

—2 

-1.6 

28.4 

43 

34-4 

109.4 

88 

70.4 

190.4 

—  I 

-0.8 

30.2 

44 

35-2 

III  .2 

89 

71.2 

192.2 

0 

0 

32.0 

45 

36.0 

II3.0 

90 

72.0 

194.0 

I 

0.8 

33-8 

46 

36.8 

II4.8 

9i 

72.8 

195.8 

2 

1.6 

35-6 

47 

37-6 

II6.6 

92 

73-6 

197.6 

3 

2.4 

37-4 

48 

38.4 

II8.4 

93 

74-4 

199.4 

4 

3-2 

39-2 

49 

39-2 

120.2 

94 

75.2 

201.2 

5 

4.0 

41.0 

50 

40.0 

122.0 

95 

76.0 

203.O 

6 

4.8 

42.8 

51 

40.8 

123.8 

96 

76.8 

204.8 

7 

5.6 

44.6 

52 

41.6 

125.6 

97 

77.6 

206.6 

8 

6.4 

46.4 

53 

42.4 

127.4 

98 

78.4 

208.4 

9 

7.2 

48.2 

54 

43-2 

129.2 

99 

79.2 

210.2 

IO 

8.0 

50.0 

55 

44.0 

I3I.O 

100 

80.0 

212.  0 

ii 

8.8 

51.8 

56 

44.8 

132.8 

101 

80.8 

213.8 

12 

9.6 

53-6 

57 

45-6 

134.6 

102 

81.6 

215.6 

13 

10.4 

55-4 

58 

46.4 

136.4 

103 

82.4 

217.4 

14 

II.  2 

57-2 

59 

47.2 

138.2 

104 

83.2 

219.2 

15 

12.0 

59-o 

60 

48.0 

140.0 

105 

84.0 

221.0 

16 

12.8 

60.8 

61 

48.8 

I4I.8 

106 

84.8 

222.8 

17 

13-6 

62.6 

62 

49.6 

143.6 

107 

85-6 

224.6 

18 

14.4 

64.4 

63 

50.4 

145-4 

108 

86.4 

226.  \ 

19 

15-2 

66.2 

64 

51.2 

147.2 

109 

87.2 

228.2 

20 

16.0 

68.0 

65 

52.0 

149-0 

110 

88.0 

230.0 

21 

16.8 

69.8 

66 

52.8 

150.8 

III 

88.8 

231.8 

22 

17-6 

71.6 

67 

53-6 

152.6 

112 

89.6 

233.& 

23 

18.4 

73.4 

68 

54-4 

154-4 

H3 

90.4 

235-4 

24 

19.2 

75.2 

69 

55.2 

156.2 

114 

91.2 

237.2 

HANDY  TABLES. 
COMPARISON  OF  THERMOMETERS — Continued. 


Celsius. 

Reaumur. 

Fahren- 
heit. 

Celsius. 

Reaumur. 

Fahren- 
heit. 

Celsius. 

Reaumur. 

Fahren- 
heit. 

»5 

Q2.0 

239-0 

127 

101.6 

260.6 

139 

III.  2 

282.2 

116 

92.8 

240.8 

128 

102.4 

262.4 

140 

112.  0 

284.0 

117 

93-6 

242.6 

129 

103.2 

264.2 

141 

112.  8 

285.8 

118 

94-4 

244.4 

130 

104.0 

266.0 

142 

II3.6 

287.6 

119 

95-2 

246.2 

131 

104.8 

267.8 

143 

II4.4 

389.4 

120 

96.0 

248.0 

132 

105.6 

269.6 

144 

II5.2 

291.2 

121 

96.8 

249.8 

133 

106.4 

271.4 

145 

116.0 

293-0 

122 

97-6 

251.6 

134 

107.2 

273.2 

146 

116.8 

294.8 

123 

98.4 

253-4 

135 

108.0 

275.0 

147 

117.6 

296.6 

124 

99.2 

255-2 

136 

108.8 

276.8 

148 

118.4 

298.4 

"5 

100.  0 

257.0 

137 

109.6 

278.6 

149 

119.2 

300.2 

126 

100.8 

258.8 

138 

110.4 

280.4 

150 

120.0 

302.O 

HANDY  TABLES. 


VII. 

DENSITIES  AND  VOLUMES  OF  WATER. 
KOPP;  CORRECTED  BY  PORTER. 


Temperature. 

Volume,  Kopp. 

Corrected  Vol- 
ume. 

Differenees. 

F. 

c. 

39-2 

4 

.OOOOO 

.OOOOO 

41.0 

5 

.00001 

.OOOOI 

24. 

51.8 

10 

.00025 

.00025 

^T" 

-Q 

34 

59.0 

15 

.00082' 

.00083 

5° 
88 

30. 

68.0 

20 

.00169 

.00171 

27 

77-0 

25 

.00284 

.00286 

JI5 

T  fjf\ 

24 

86.0 

3° 

.00423 

.00425 

J39 

ff.r 

22 

95  o 

35 

.00583 

.00586 

IOI 

TQT 

2O 

104.0 

40 

.00768 

.00767 

1  0  1 
onn 

19 

113.0 

45 

.00967 

.00967 

4\J\J 

19 

122.  0 

50 

.01190 

.01186 

219 

2<77 

18 

131.0 

55 

.01423 

.01423 

•"O/ 

18 

140.0 

60 

.01672 

.01678 

255 

0*7'? 

18 

149.0 
150.0 

65 
70 

.01943 
.02238 

.01951 
.02241 

273 
290 

17 
17 

167.0 

75 

.02554 

.02548 

3°7 

AAJ 

17 

176.0 

80 

.02871 

.02872 

324 

17 

185.0 

85 

.03202 

.03213 

34  * 

16 

194.0 

90 

.03553 

.03570 

357 

0*7*3 

16 

203.0 

95 

.03921 

•03943 

373 

oRn 

16 

212.0 

IOO 

.04312 

.04332 

JUV 

WEIGHTS  AND  VOLUMES. 


Ratio  of 

Ratio  of 

Ratio  of 

nperature, 

volume  to 
that  of 
equal 
weight  at 
maximum 

Weight 
of  a 
cubic 
foot. 

nperature 

volume  to 
that  of 
equal 
weight  at 
maximum 

Weight 
of  a 
cubic 
foot. 

volume  to 
that  of 
equal 
weight  at 
maximum 

Weight 
of  a 
cubic 
foot. 

t 

density. 

£ 

density. 

H 

density. 

Fahr. 

Lbs. 

Fahr. 

Lbs. 

Fahr. 

Lbs. 

32-° 

.000129 

62.417 

210.° 

.04226 

59.894 

39°.° 

•15538 

54.030 

39-i 

.000000 

62.425 

212. 

.04312 

59-707 

400. 

.16366 

53-635 

40. 

.000004 

62.423 

220. 

.04668 

59.641 

410. 

.17218 

53-255 

5°- 

.000253 

62.409 

230. 

.05142 

59-372 

420. 

.18090 

52.862 

60. 

.000929 

62.367 

240. 

•05633 

59.096 

430. 

.18982 

52.466] 

70. 

.001981 

62.302 

250. 

.06144 

58.812 

44o. 

.19898 

52.065 

80. 

.00332 

62.218 

260. 

.06679 

58.5^7 

45°- 

.20833 

51.662 

90. 

.00492 

62.119 

270. 

.07233 

58.214 

460. 

.21790 

51-256 

too. 
no. 

.00686 
.00902 

62.000 
61.867 

280. 
290. 

.07809 
.08405 

57-903 
57-585 

£ 

.22767 
•23766 

50.848 
50.438 

120. 

.01143 

61.720 

300. 

.09023 

57-259 

49o. 

•24785 

50.026 

130. 

.01411 

61.556 

3IO. 

.09661 

56.925 

500. 

.25828 

49.611 

140. 

.01690 

61.388 

320. 

•  10323 

56.584 

510. 

.26892 

49-!95 

ISO- 

.01995 

61.204 

33°. 

.11005 

56.236 

520. 

•27975 

48.778 

160. 

.02324 

61.007 

34°. 

.  11706 

55-883 

53°. 

.  29080 

48.360 

170. 

.02671 

60  .  801 

350. 

.12431 

55-523 

540. 

.  30204 

47-941 

180. 

.03033 

60.587 

360. 

•13175 

55-158 

550. 

•3I354 

47-521 

190. 

.03411 

60.366 

370- 

.13042 

54-787 

200. 

.03807 

60.136 

380. 

•  M729 

54-4" 

HANDY   TABLES. 


29 


VIII. 

TEMPERATURES  AND  PRESSURES,  SATURATED  STEAM. 
IN  METRIC  MEASURES  AND  FROM   REGNAULT. 


»j 

(j 

3 
rt 

STEAM-PRESSURE. 

fl 

STEAM-PRESSURE. 

ft 

a 

• 

In  Centimetres. 

In  Atmospheres 

1 

In  Centimetres. 

In  Atmospheres 

H 

h 

-  32°  C 

0.0320 

0.0004 

+  14°C 

.1908 

0.016 

31 

0.0352 

0.0005 

15 

.2699 

0.017 

30 

0.0386 

0.0005 

16 

.3536 

O.OlS 

29 

0.0424 

0.0006 

17 

.4421 

0.019 

28 

0.0464 

0.0006 

18 

•5357 

0.020 

27 

0.0508 

0.0007 

19 

.6346 

0.022 

26 

0-0555 

0.0007 

20 

•7391 

0.023 

25 

0.0605 

0.0008 

21 

.8495 

0.024 

24 

0.0660 

0.0009 

22 

•9659 

O.O26 

23 

0.0719 

0.0009 

23 

2.0888 

0.028 

22 

0.0783 

O.OOIO 

24 

2.2184 

O.O29 

21 

0.0853 

O.OOII 

25 

2.3550 

0.031 

20 

0.0927 

0.0012 

26 

2.4988 

0.033 

19 

o.  1008 

0.0013 

27 

2.5505 

0.034 

18 

0.1095 

0.0014 

28 

2.8101 

0.037 

17 

o.  1189 

0.0015 

29 

2.9782 

0.039 

16 

0.1290 

0.0017 

30 

3.1548 

0.042 

15 

0.1400 

0.0018 

31 

3.3406 

0.044 

14 

0.1518 

0.0020 

32 

3-5359 

0.047 

13 

0.1646 

0.0022 

33 

3-74" 

0.049 

12 

0.1783 

O.OO24 

34 

3.9565 

0.052 

II 

0.1933 

0.0025 

35 

4.1827 

0-055 

10 

0.2093 

O.OO27 

36 

4.4201 

0.058 

9 

0.2267 

0.0030 

37 

4.6691 

0.061 

8 

0.2455 

O.OO32 

38 

4.9302 

0.065 

7 

0.2658 

0.0035 

39 

5.2039 

0.068 

6 

0.2876 

O.OO38 

40 

5.4906 

0.072 

5 

0.3113 

0.0041 

41 

5.7910 

0.076 

4 

0.3368 

0.0044 

42 

6.1055 

0.080 

3 

0.3644 

0.0048 

43 

6.4346 

0.085 

2 

0.3941 

0.0052 

44 

6.7790 

0.089 

I 

0.4263 

O.OO56 

45 

7-I391 

0.094 

O 

0.4600 

0.0061 

46 

7.5158 

0.099 

+   1 

0.4940 

0.0065 

47 

7.9093 

0.104 

2 

0.5302 

0.0070 

48 

8.3204 

0.109 

3 

0.5687 

0.0073 

49 

8.7499 

0.115 

4 

0.6097 

0.0080 

50 

9.1982 

O.I2I 

5 

0.6534 

0.0086 

51 

9.6661 

0.127 

6 

0.6998 

0.0092 

52 

10.1543 

0.134 

7 

0.7492 

0.0199 

53 

10.6636 

0.140 

8 

0.8017 

0.0107 

54 

11.1945 

0.147 

9 

0.8574 

O.OII 

55 

11.7478 

0.155 

10 

0.9165 

O.OI2 

56 

12.3244 

O.I63 

ii 

0.9792 

0.013 

57 

12.9251 

O.I7O 

12 

1.0457 

O.OI4 

58 

13.5505 

0.178 

13 

1.1162 

0.015 

59 

14.2015 

0.187 

HANDY   TABLES. 


TEMPERATURES  AND  PRESSURES,  SATURATED  STEAM — Continued. 


oF 

i 

STEAM-PRESSURE. 

a 

STEAM-PRESSURE. 

1 

I 

Q 

6 

In  Centimetres. 

In  Atmospheres 

S 

<u 

In  Centimetres. 

In  Atmospheres 

H 

H 

-|-  60°  C. 

14.8791 

0.196 

H-IIOOC 

107.537 

.415 

61 

15.5839 

0.205 

III 

III.  209 

•463 

62 

16.3170 

0.215 

112 

114.983 

•513 

63 

17.0791 

0.225 

113 

118.861 

.564 

64 

17.8714 

0.235 

114 

122.847 

.616 

65 

18.6945 

0.246 

115 

126.941 

.670 

66 

19.5496 

0.257 

116 

I3LI47 

.726 

67 

20.4376 

0.267 

117 

I35.466 

.782 

68 

21.3596 

0.281 

118 

I39.902 

.841 

69 

22.3165 

0.294 

119 

144.455 

.901 

70 

23.3093 

0.306 

120 

149.128 

.962 

71 

24-3393 

0.320 

121 

153.925 

2.025 

72 

25-4073 

0-334 

122 

158,847 

2.091 

73 

26.5147 

0-349 

123 

163.896 

2.157 

74 

27.6624 

0.364 

124 

169.076 

2.225 

75 

28.8517 

0.380 

125 

174-388 

2.295 

76 

30.0838 

0.396 

126 

T79.835 

2.366 

77 

31  .  3600 

0.414 

I2/ 

185.420 

2.430 

78 

32.6811 

0.430 

128 

191.147 

2.515 

79 

34.0488 

0.448 

129 

197.015 

2.592 

80 

35.4643 

0.466 

130 

203.028 

2.671 

81 

36.9287 

0.486 

131 

209.  194 

2.753 

82 

38.4435 

0.506 

132 

215.503 

2.836 

83 

40.0101 

0.526 

133 

221.969 

2.921 

84 

41.6298 

0.548 

134 

228.592 

3.008 

85 

43.3041 

0.570 

135 

235.373 

3.097 

86 

45.0344 

0.593 

I36 

242.316 

3-188 

87 

46.8221 

0.616 

137 

249.423 

3.282 

88 

48.6687 

0.640 

138 

256.700 

3.378 

89 

50.5759 

0.665 

139 

264.144 

3.476 

90 

52.5450 

0.691 

140 

271.763 

3.576 

91 

54.5778 

0.719 

141 

279-557 

3.678 

92 

56.6757 

0.746 

142 

287.530 

3.783 

93 

58.8406 

0.774 

143 

295.686 

3.890 

94 

61.0740 

0.804 

144 

304  .  026 

4.000 

95 

63.3778 

0.834 

145 

312.555 

4.H3 

96 

65-7535 

0.865 

146 

321.274 

4.227 

97 

68.2029 

0.897 

147 

330.187 

4-344 

98 

70.7280 

0.931 

I48 

339.298 

4.464 

99 

73.3305 

0.965 

149 

348.609 

4.587 

100 

76.000 

I.OOO 

150 

358.123 

4-712 

IOI 

76.7590 

1.036 

151 

367.843 

4.840 

102 

81.6010 

1.074 

152 

377-774 

4.971 

103 

84.5280 

1.  112 

153 

387-918 

5.104 

104 

87.5410 

I.I52 

154 

398.277 

5.240 

105 

90.6410 

•193 

155 

408  .  856 

5.380 

106 

93-8310 

.235 

I56 

419.659 

5-522 

107 

97.1140 

.278 

157 

430.688 

5.667 

108 

100.4910 

,322 

158 

44L945 

5-815 

109 

103.965 

.368 

!59 

453.436 

5.966 

HANDY   TABLES. 


TEMPERATURES  AND  PRESSURES,  SATURATED  STEAM  ^Continued. 


£ 

s 

STEAM-PRESSURE. 

<_( 

STEAM-PRESSURE. 

2 

S, 

! 

In  Centimetres. 

In  Atmospheres 

1 

In  Centimetres. 

In  Atmospheres 

-J-i6o°(7. 

465.162 

6.120 

+196°  C. 

1074.595 

14.139 

161 

477.128 

6.278 

197 

1097.500 

14.441 

162 

6.439 

198 

1120.982 

14.749 

163 

501.791 

6.603 

199 

1144.746 

15.062 

164 

5M.497 

6.770 

200 

1168.896 

15-380 

165 

527.454 

6.940 

201 

"93.437 

15.703 

1  66 

540.669 

7.114 

202 

1218.369 

16.031 

167 

554.143 

7.291 

203 

1243.700 

16.364 

168 

567.882 

7-472 

2O4 

1269.430 

16.703 

169 

581.890 

7.656 

205 

1295.566 

17.047 

170 

596.166 

7.844 

206 

1322.112 

17.396 

171 

610.719 

8.036 

207 

1349.075 

I7./5I 

172 

625.548 

8.231 

208 

1376.453 

18.111 

173 

640.660 

8.430 

209 

1404.252 

18.477 

174 

656.055 

8.632 

210 

1432.480 

18.848 

175 

67L743 

8.839 

211 

1461.132 

19.226 

176 

687.722 

9.049 

212 

1490.222 

19.608 

177 

703.997 

9.263 

213 

1519.748 

19.997 

178 

720.572 

9.481 

214 

I549.7I7 

20.391 

179 

737.452 

9.703 

215 

1580.133 

20  .791 

180 

754.639 

9.929 

216 

1610.994 

21.197 

181 

772.137 

10.150 

217 

1642.315 

21.690 

182 

789.952 

10.394 

218 

1674.090 

22.O27 

183 

808.084 

10.633 

219 

1706.329 

22.452 

184 

826.540 

10.876 

220 

1739.036 

22.882 

185 

845.323 

11.123 

221 

1772.213 

23-3I9 

186 

864.435 

H.374 

222 

1805.864 

23.761 

187 

883.882 

I  I  .  630 

223 

1839.994 

24.210 

188 

903.668 

11.885 

224 

1874-607 

24.666 

189 

923.795 

12.155 

225 

1909.704 

25.128 

190 

944.270 

12.425 

226 

1945.292 

25.  596 

191 

965.093 

12.699 

227 

1981.376 

26.071 

192 

986.271 

12.977 

228 

2017.961 

26.552 

193 

1007.804 

13.261 

229 

2055.048 

27.040 

194 

1029.701 

13-549 

230 

2092.640 

27.535 

195 

1051.963 

13.842        1 

HANDY   TABLES. 


IX. 

METRIC  STEAM  AND  WORK  TABLE. 


Abso?ute  pres- 

Specific volumes 

w      26127.34 

TIT        _ 

sures  in  Atmos 
phere. 

v«  in  Cu.  meters. 

Product  pflve. 

1000  pev. 

vv  .  pa. 

O.I 

14.504 

1.450 

18.010 

1.801 

0.2 

7.525 

1.505 

17.418 

3.483 

0.3 

5.128 

1.540 

16.960 

5.088 

0.4 

3.908 

1.560 

16.750 

6.700 

0.5 

3.165 

1.580 

16.530 

8.265 

0.6 

2.665 

I.6OO 

16.339 

9-803 

0.7 

2.304 

1.610 

16.230 

11.361 

0.8 

2.031 

1.620 

16.  120 

12.896 

o.g 

.818 

1.630 

16.020 

14.418 

.0 

.646 

1.646 

15.870 

15-870 

.1 

.505 

1-655 

15.780 

17.385 

.2 

.386 

1.663 

15.710 

18.852 

.3 

.285 

1.670 

15.640 

20.332 

•4 

.199 

i.  680 

15.540 

21.756 

•  5 

.123 

1.684 

15.510 

23  •  265 

.6 

•057 

1.691 

15.450 

24  .  720 

•  7 

0.999 

1.699 

15.370 

26.129 

.8 

0.946 

1.703 

15.340 

27.612 

•9 

0.899 

1.708 

15.290 

29.051 

2.0 

0.857 

1.714 

15.243 

30.486 

2.1 

0.819 

1.718 

15.208 

31-937 

2.2 

0.784 

1-725 

15.146 

33.321 

2-3 

0-751 

1.727 

15.128 

34-794 

2.4 

0.722 

1-733 

I5.076 

36.182 

2.5 

0.695 

1.741 

15.002 

37.505 

2.6 

0.670 

1.742 

14.990 

38.974 

2.7 

0.646 

1.744 

14.970 

40.190 

2.8 

0.625 

1-750 

14.929 

41.801 

2.9 

0.604 

1.752 

14.921 

43-271 

3.0 

0.586 

1.758 

I4.b6l 

44.583 

3.1 

0.568 

1.761 

I4-838 

4S-99& 

3.2 

0-551 

1.763 

I4.8l8 

47.417 

3.3 

0-535 

1.765 

14.790 

48  807 

3.4 

0.521 

1.771 

14-749 

50.146 

3.5 

0.507 

1-774 

14.723 

5L330 

3-6 

0.493 

1-775 

14.720 

52.992 

3-7 

0.481 

1.780 

14.680 

54.316 

3-8 

0.469 

1.782 

14.660 

55.708 

3-9 

0.458 

1.786 

14  .  630 

57-057 

4.0 

0.447 

1.788 

14.61 

58.440 

4.1 

0.437 

1.792 

14.58 

59.778 

4.2 

0.427 

1-793 

14.56 

61.152 

4-3 

0.418 

1.797 

14-53 

62.479 

4.4 

0.409 

1.799 

14.52 

63.888 

HANDY   TABLES. 
METRIC  STEAM  AND  WORK  TABLE — Continued. 


33 


Absolute  pres- 
ure   pe  in   At- 
mospheres. 

Specific  volumes 
v,  in  Cu.  meters. 

Product  p,  v.. 

Wj_   26137.34 
**  1000  p.  v. 

W.jv 

4-5 

0.400 

.800 

14.51 

65-295 

4-6 

0.392 

.803 

14.49 

66.654 

4-7 

0.384 

.805 

14.45 

67.915 

4.8 

0:377 

.810 

14-43 

69.264 

4.9 

0.370 

.813 

14.41 

70.609 

5.0 

Oo63 

.815 

14.39 

7L950 

5-i 

0.356 

.816 

14.38 

73.338 

5-2 

0.350 

.820 

14.36 

74.672 

1        5-3 

0.343 

.821 

14.35 

76.055 

5-4 

0-337 

.823 

14.33 

77.382 

5-5 

0.332 

.825 

14.31 

78.705 

5-6 

0.326 

.826 

14.30 

80.080 

5-7 

0.321 

.829 

14.26 

81.282 

5-8 

0.316 

•833 

14.25 

82.650 

5-9 

0.311 

.835 

14.24 

84.016 

6.0 

0.306 

.836 

14.23 

85.380 

6.25 

0.294 

-838 

14.21 

88.812 

6-5 

0.284 

.845 

14.16 

92.040 

6.75 

0.273 

.848 

14-13 

95-377 

7.0 

0.265 

•855 

14.10 

98.700 

7-25 

0.256 

.856 

14.07 

100.997 

7-5 

0.248 

.860 

14.04 

105.300 

7-75 

0.241 

.867 

13.99 

108.422 

8.0 

0.234 

.872 

13.96 

111.680 

8.25 

0.227 

-873 

13-95 

114.077 

8-5 

0.221 

.878 

13.91 

118.235 

8-75 

0.215 

.881 

13.89 

121-537 

9.0 

O.2O9 

.883 

13.86 

154.740 

9-25 

0.204 

.887 

13.84 

128.020 

9-5 

0.199 

.891 

13.81 

131.195 

9-75 

0.194 

-893 

13-80 

134-550 

10.  0 

O.igO 

.900 

13-75 

137-500 

34 


HANDY   TABLES. 


t.  The  tempera- 
adopting  the  for° 
on  are  separately 
ure  is  sufficiently 

spnnod  ui  'uinnoBA  B  3AoqB  aincsajj 

8, 

M  N  ro  ^  i/^vo  e-xco  O\  O 

__ 

f       ^VOK 

*  Weisbach's  Mechanics,  vol  ii.,  part  ii.,  Dubois'  translation.  N.  Y.:  J.  Wiley  &  Sons.  1884. 

"I    " 

VOLUME. 

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The  column  headed  "  £7"  in  the  table  of  the  properties  of 
saturated  steam  is  useful  for  reducing  the  performance  of  differ- 
ent boilers  to  a  common  standard — this  standard  being  that 
most  generally  accepted  by  engineers :  the  equivalent  evapora- 
tion at  atmospheric  pressure  and  the  temperature  of  boiling 
water,  or,  as  it  is  frequently  called,  the  evaporation  from  and  at 
212°.  In  the  table  it  is  assumed  that  the  temperature  of  the 


feed-water   is   32°,    and    an  auxiliary  table    is    added, 
corrections  for  any  temperature  of  feed  from  32°  to  2 12°. 


giving 


CORRECTION  FOR  TOTAL  HEAT  IN  UNITS  OF  EVAPORATION. 


Tempera- 
ture of 
feed,  Fah- 
renheit 
degrees. 

Correction. 

Tempera- 
ture of 
feed,  Fah- 
renheit 
degrees. 

Correction. 

Tempera- 
ture of 
feed,  Fah- 
renheit 
degrees. 

Correction. 

Tempera- 
ture of 
feed,  Fah- 
renheit 
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Correction. 

1 
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rt 
1 

1 

8 

a 

rt 

be 
.2 

a,' 

Q. 

3 

2 

g 

•o 

w 

a 

_Q 

s 

a 

• 

1 

J 

1 

a 

2 

I 

. 

1 

0 

Ji 

E 

5 

i 

C- 

- 

1 

QUANTITY. 

Pounds  per  square  foot. 

Inches  of  mercury,  at  32°  Fahr 

istilled  water,  at  temperature  of 
density. 

d 
I 

< 

Umosphere,  in  pounds  per  squa: 

Fahrenheit's  scales. 

ilute  scale,  Fahrenheit  degrees. 

to  raise  the  temperature  of  the 
32°  to  t°. 

to  change  the  water  into  steam, 
latent  heat.) 

o  overcome  the  pressure  of  the  s 
medium.  (External  latent  heat 

t  of  evaporation,  under  constant 

otal  heat  of  evaporation  above  3 

vaporation  per  pound  of  steam, 
in  units  of  evaporation. 

Feet  of  d 

bove  the  j 

1 

? 
I 

1 
1 

a 

1 
1 

1 

c 

H 

1  heat  of  e 

<; 

H 

I-J 

2 

o 

•rannoBA  ^  aAoqy 

•sunn  luuuaqi  qsnug 

UI  UIB31S  JO  puiiod  J3J 

H 

JJ 

I             j 

3 

0 

| 

V 

44 


HANDY   TABLES. 


T    1 

sT" 

o^^rrj          to 

IF 

+ 

°w  0-  m>  § 

vS 

•^ 

w 

S 

M?  1  2  o 
0+^3  + 

FORMULA. 

X 

s»   X 

g. 

u 

vg 

11 
1 

II 

<0 

I 
X 

<J 

2?.?^ 
|i|2i' 

Cfl    rts  O   p    M 

^3 

X 

s 

^ 

fc  p8  e^e 

8    •  v  8 

.* 

1 

*1 

M 

ci 

o  °     fa-f 

^ 

II 

M                  °° 

§ 

s    f 

K 

II       11 

C 

a        & 

c 

i 

. 

Cj 

^ 

H 

• 

r 

c« 

£ 

g 

^ 

s 

I 

E 

« 

3 

2 

1 

•o 

** 

^S  RELATING  TO 

ration,  per  cubic  foot  c 

steam,  in  pounds. 

er,  in  pounds,  at  tempe 

am,  in  cubic  feet. 

ume  of  equal  weight  ol 
of  maximum  density. 

er,  at  temperature  7",  t 
iture  of  maximum  dens 

a 

rt 

"o 

i 

8 

11 

u 

1    | 

1 

1 
u 

s 

o 
1 

Sg 

11 

t        3 

rt 

.2 

§ 

SE 

12 

O1 

^ 

1 

•o 

& 

tn  Si 

•°£ 

*j 

rt 

o 

•J 

*O  rt 

*s.^ 

C 

O 

0 

a  fc 

fi  ^ 

rt 

«2 

Srt 

1*3 

"d 

.0 

"o  ? 

*0  3 

'i 

3 
u 

0 

•sl 

£™ 

ctf 

o 

o  ° 

! 

0 

i 

i 

o 
o 

1 

4 

1 

8 

1 

1 

£ 

HANDY   TABLES. 


45 


ss 


O    vo    K   «o  O    u->     O   «o  O   to  o>     •«•  o  -»•  :>  m    OO   moo   rnc^     dt^Mr^M     «OM\OM 
n    fifOWWM      «OO  ooo    oo  S.  r^>0  vo     inui^--*-r^m«M««      OOO  c 


Nr^ts,      N    Ix.  N    c-x  M     so    n  so    M    iA     O    "^  O    ""*  O*     ^  O  v  O1  "1    CO    f)  fv  r^joo       ro 
ONOO    oo  tx  ts.\o  NO     m  m  -^  •**•  fo    co  w  w  «  o     o  9^  2^99  °°     rx  ^^c  -o  m    irj 

HM    MMMMM    HMWHW    M  M  M  M  IH    M  Q  O  0  O    OOOOO    O 


^f-    n  NO  O  m  O     vj  Q  vi  O  ^    O*  •**•  O*  ^-oo     f"J  f)  moo  w      hs  w  tx  w  \o 

J?  5?SS55    B8?W   STST'S'S!?  ????!?  2  2  5  5  2 


I    M    oomropit^    NtowtoM    VOHVOMIO    o«oO>oo>    ^-o 
0  mNN-»o     00  ooo  oo     t--  tovo  vomio^-^mN     ww 

8  o    «  «  «  N.  «  w.  w.  i M.  i  *:  M.  H.  t  H.  M.  w.  H.  M.  M.  M.  ^  *: 


o'o1 


8  *r 


to,    ^  o  moo  m  oo  moo  mto    wtonioM    VOMVOMIO    o>oO>oo    ^o^omoo  moo  moo     m 

N       <M    ~    M   O    O       O  OOO  OO   to,     tovo  VOlOJO     •^Tj-mmo       NMMOO     OOO  OOlotovovoioio-*     •*• 

N    N  «  N  IN  M    1HMMKM    MWMMM    MMMINM    MMMMQ    OOOOO    OOOOO    0 


*^    MVOO*OO     lOO^oO-^    O-^-O  ^-oo      rooo  moo  w      tow^wvo     HIVO«VOO     too>oo»o     O 

SC4  M  H*  o  O     O  ooo  ootxvovoioiO'*-    •^•mmww      MMQOO    Ooo  ootorovovoioio-^-     ^r 
ONNNN         WMM-11         M     M     «     «     M         MMMMM        MM«H.S         OOOOO         OOOOOO 


a  ^ 


vS        °- 


&  •? 


ro    M 


SO  ^OO   f^OO      *^ioo   rooo   01      ro,c*Co,e*^O      M\O»H*OO      lOOu^C"^ 
M  «  0   0  0-    Ooo  oor^tx\OvOiom-«-     -*rofONw      «i-o5o 


*00    •^•o<**>Ofooo  rooo  mto,    ct^d 
t^>0     >OIOIOT»-TI-     en  MWN«      MOO 


OO 


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c*to.M    vo  M  vo  M  10     O 


vo  M  10 


^     MVOO'OO      i^O^O1^     O^O^ro     mo   moo   W      loct^wvo      MVO^VOO      iOO»oO^o     O 
HI     wooooooooto  tovo     loio^-'i-m    mNN«M     ooo  ooo    oo  to  tovo  vo     10  10  *  •*  m    m 

CI          WNNWI-I  IHWW1-11-I  WWMMM          MMMHIH          M      PH      0      O      O  OOOOO  OOOOO          C 


ci     gv*oo  moo     moo  moo  N     tocttoNvo     MVOMVOO     looioo-*    O  •*•  O  ^oo     moo  moo  m  oo 
HI     OOo  ooo    oo  to  tovo  vo     toio^^m    mc4C*HiM     OOO  ooo     t^  t^vo  voio    lo^-^-mro    «' 

M         WWHIHIHl         MMH.MM         MMMMHI         MMMHM         MMOOO         OOOOO         OOOOO         O 


M    oomtowto    MtoMtoM    VOHVOMIO    Oioo>oo    ^-O^omoo  moo  coto    wto«to«     to 
H     ooo  ooo    oo  ^  tovo  vo     loio^^m    mMwwS     oo  ooo  oo     to  to,vo  voio    to-'j-'^-m'-)    « 

(1         «««««         WH.MH.H1          M     M     H     M     HI          MMMMM         M^     O    O     O         O     O     O     OO         OOOOO         O 


MUiOto    omO«oo    •*O'*omoo  rooo  mto 

'  » 


^2? 


•«r    wvoo>oo     ioO<oO-*    O'J-o  ^oo     moo  moo  ct     tonton^     mo«voo     motoO"'*    O 
000  Ooo  oo     t^  tovo  vem^'S-mmM     INMMQO     O  ooo  oo  to    IO.VG  voioio    -*-«-mm«     S 


V 


VC    •*  M  to      10  m  M    IOVO       •4-MOtolO      ro  w  00  >O    ••*•      N    O    to  IO  ro      MOOVO^M       OtolOCOM 


HANDY  TABLES. 


XIV. 
COMPOSITION  OF  VARIOUS   FUELS  OF  THE   UNITED  STATES. 


C. 

H.       0. 

M 

-S1. 

Mois- 
ture. 

Ash. 

Spec. 
Grav. 

78.6 

2.5     1.7 

0.8 

1.2 

14.8 

i  .45 

Rhode  Island          "            

8s  8 

ge 

6  o 

78 

North  Carolina       **          

83.  i 

7.8 

9-  * 

Welsh                      " 

Maryland  Semi-bituminous  

80.5 

4-5     2.7 

i.i 

I  .7 

8-3 

75  8 

Qg      8 

J  ? 

Indiana                "                         

28.0 

62.6 

35-5 

I  .Q 

.30 

58    2 

36  6 

Kentucky  (Cannel  )  Bituminous  

48.4 

48.8 

08 

•25 

'45 

56  5 

42.6 

i  .0 

1.2 

I  .2 

41  o 

18  6 

California  and  Oregon  Lignite  

50.1 

3-9  13-7 

0.9 

i-5 

I6.7 

13.2 

1.32 

STATE. 

COAL. 
KIND  OF  COAL. 

Per  Cent,  of 
Ash. 

THEORETICAL  VALUE. 

In  Heat 
Units. 

In  Pounds 
of  Water 
Evaporated. 

3-49 
6.11? 
2.90 

15.02 
6.50 
10.77 
5-oo 
5-6o 
9-5o 
2-75 

2.00 
14.80 
7.00 

5.20 

5-6o 
5-50 

H 

6.00 
13.98 
5-oo 
9-25 
4-50 
4-5° 
3-4° 

14,199 
13,535 
14,221 
I3>T43 
13,368 
I3ii55 
14,021 
14,265 
12,324 
I4,39i 
15,198 
13,360 
9,326 
13,025 
I3,"3 
12,659 
13,588 
14,146 
13,097 
12,226 
9,215 
I3,562 
13,866 
12,962 
",55i 
20,746 

14.70 
14.01 
.    14.72 
13.60 
13-84 
13.62 
14-  5  1 
14.76 
12.75 
14.89 
16.76 
13-84 
9-65 
13.48 
13-58 
13.10 
14-38 
14.64 
I3-56 
12.65 
9-54 
14.04 
H-35 
13-41 
11.96 
21.47 

U                                                                                 " 

H 

Cannel 

M 

Connelsville  

« 
(« 

Semi-bituminous  
Stone's  Gas  

(i 

Youghiogheny.  ...  

Brown  

Caking 

Cannel      

H 

l4 

Illinois 

Bureau  County  

H 

Indiana  

Block  
Caking  

44 

Colorado 

ii 

Texas 

41 

If 

ennsy  vania 

HANDY   TABLES. 


ANALYSES   OF  ASH. 


Specific 
Grav. 

Color 
of  Ash. 

Silica. 

Alum- 
ina. 

Oxide 

Iron. 

Lime. 

Mag- 
nesia. 

Loss. 

Acids 
S.&P. 

Pennsylvania  Anthracite  
Bituminous  
Welsh  Anthracite 

1-559 
1-372 

Reddish 
Buff. 
Gray. 

45-6 

76.O 

42.75 

21.  OO 

44  8 

ts 

1.41 

Q-33 
trace 

0.48 
0.40 

2   Q7 

37« 

52.0 

3-7 

1.  1 

5.O2 

11.6 

5-8 

2.6 

33  « 

48 


HANDY   TABLES. 


XV. 

HORSE-POWER   PER   POUND  MEAN   PRESSURE. 


Diameter  of 
Cylinder. 
Inches. 

SPEED  OF  PISTON  IN  FEET  PER  MINUTE. 

100 

240 

300 

350 

400 

450 

500 

550 

600 

650 

760 

4 

.038 

.091 

.114 

•  133 

.152 

.171 

.19 

.209 

.228 

.247 

.285 

4* 

.048 

•  us 

.144 

.168 

.192 

.216 

.24 

.264 

.288 

.312 

.360 

5 

.06 

•  144 

.18 

.21 

•  24 

.27 

•30 

•33 

•36 

•39 

•  450 

5* 

.072 

.216 

.252 

.288 

•  324 

.36 

•396 

•  432 

.468 

•540 

6 

.086 

.102 

.205 

.245 

.256 
•  307 

.299 
•391 

•  342 
•  409 

.385 
.464- 

.428 
•  512 

.471 
•563 

:l\l 

loi 

.64I 
.800 

7 

.Il6 

.279 

-348 

.408 

.466 

•  524 

.641 

•699 

'756 

.874 

7* 

j-j  A 

.321 

.401 

.468 

•534 

.602 

.660 

•735 

.802 

.869 

.002 

8 

•IS2 

-365 

.456 

•532 

.608 

.685 

.761 

•837 

.912 

.989 

.121 

8} 

.172 

•  413 

.516 

.602 

.688 

-774 

.86 

.946 

1.032 

.118 

.290 

9 

.192 

.462 

.674 

.770 

.866 

•963 

•°59 

1.154 

.251 

•444 

9t 

.215 

•  5*5 

.644 

.751 

.859 

.966 

.074 

.181 

1.288 

•395 

.610 

JO 

.238 

•571 

.714 

-833 

•952 

1.071 

.190 

•309 

1.428 

•547 

-785 

IO.J- 

.262 

•  63 

.787 

.919 

1.050 

1.181 

•3T3 

•444 

1-575 

.706 

.960 

II 

.288 

.691 

.864 

I.OOS 

1.152 

1.296 

•44 

-584 

1.728 

.872   .i6o 

11* 

•314 

•754 

•943 

I.I 

1-257 

1.414 

•572 

.729 

1.886 

•043   -357 

12 

•342 

.820 

1.025 
1.206 

I-I95 
1  .407 

!'!o8 

1.540 
i  .800 

.708 

.880 

2.050 

.222 

•564 

14 

.  4O2 

.466 

1.119 

1.398 

1.631 

1^864 

2-097 

2-331 

•564 

2-797 

3.029 

3-495 

15 

•535 

1.285 

i.  606 

1.873 

2.131 

2.409 

2.677 

•945 

3-212 

3-479 

4.004 

16 

.609 

1.461 

1.827 

2.I3I 

2-436 

2.741 

3-°45 

3-349 

3-654 

3-958 

4-567 

17 

•  685 

1.643 

2.054 

2.396 

2-739 

3.081 

3-424 

3.766 

4.108 

4.450   5.135 

18 

.771 

1.849 

2.312 

2.697 

3-083 

3-468 

3-854 

4-239 

4.624 

5.009   5.780 

ig 

.859 

2.061 

2-577 

3.006 

3-436 

3-865 

4-295 

4.724 

5-I54 

5-583  i  6.442 

20 

•952 

2.292 

2.855 

3-331 

3.807 

4.285 

4-759 

5-234 

5-73i 

6.186  !  7.138 

21 

.049 

2.518 

3.148 

4.197 

4.722 

5-247 

5-771 

6.296 

6.820   7.860 

22 

.152 

2.764 

3-455 

4.031 

4.607 

5-183 

5-759 

6-334 

6.911 

7.486 

8.638 

23 

.259 

3.021 

3-776 

4.405 

5-035 

5.664 

6.294 

6.923 

7-552 

8.181 

9.44 

24 

•370 

3.289 

4.111 

4-797 

5-482 

6.167 

6-853 

7.538 

8.223 

8.908  '10.270. 

25 

.487 

3-569 

4-461 

5-105 

5-948 

6.692 

7-436 

8.179 

8923 

9.566  11.053 

26 

.609 

3.861 

4.826 

5.630 

6-435 

7.239 

8.044 

8.848 

9-652 

10.456  12.065 

27 

•733 

4-159 

5-199 

6.066 

6-932 

7-799 

8.666 

9-532 

10  399 

11.265  12.998 

28 

.865 

4-477 

5-596 

6.529 

7.462 

8-395 

9-328 

10.261 

11.193 

12.125  13.991 

29 

.002 

4.805 

6.006 

7.007 

8.008 

9.009 

10.01 

II.  Oil 

12.012 

13.013  15.015 

3° 

.142 

6.426 

7-497 

8.568 

9-639 

10.71 

11.781 

12.852 

13.923  16.065 

3i 

.288 

5^486 

6.865 

8.001  ' 

9.144 

10.287 

"•43 

12-573 

13.716 

14.866  17.145 

32 
33 

-436 

59° 

5.846 
6.216 

7.308 
7.770 

8.526 
9.065 

9-744 
10.360 

10.962 
11-655 

2.18 
2-959 

I3-398 

14.616 
15-54 

15.834  18.270 
16.835  19.425 

34 
35 

-746 
.914 

6-59 
6-993 

8.238 
8.742 

9.611 
10.199 

10.984 
11.656 

12-357 

3-73 
4-57 

15-103 
16.027 

16.476 
17.484 

17.849  20.595 
18.941  21.855 

36 

3.084 

7.401 

9.252 

10.794 

12.336 

13-878 

5-42 

16.962 

18.504 

20.046  23.130 

3-253 

7.819 

9-774 

11.403 

13.032 

14.861 

6.29 

I7-9I9 

19.548 

21.177  24  433 

38 

8.246 

10.308 

12.026 

I3.744 

15.462 

7.18 

18.898 

2O.6l6 

22.334  25.770 

39 

3.620 

8.648 

10.86 

12.67 

14.48 

16.29 

8.1 

19-91 

21.62 

23-53   27.150 

40 
41 

3.808 
4.002 

9.139 
9.604 

11.424 
12.006 

13-328 
14.007 

15-232 
16.008 

17.136 
18.009 

19.04 
20.00 

20.944 

22.011 

22.848 
24.012 

24.752  128.560 
26.013  30,015 

42 

4.198 

10.065 

12.594 

14.693 

16.792 

18.901 

20.99 

23-089 

25.188 

27.287 

31-485 

43 

4.40 

10.56 

13.20 

17.6 

19.8 

22.00 

24.2 

26.4 

28.6 

33-00 

44 

4.606 

11.046  13.818 

16.121 

18.424 

20.727 

23.03 

25-333 

27.636 

29.939 

34-545 

8 

47 

4.818 
5-043 
5-256 

11.563  14.454 
12.086  15.128 
12.614  '5-768 

16.863 
17.626 

18.396 

19.272 
20.144 
21.024 

21.681 
22.662 
23-652 

24.09 
25.18 
26.28 

27.698 
28.908 

28.908 
30.216 
31.536 

32-754 
34.164 

36.135 
37.770 
39.420 

48 

5.482 

12.846 

16.446 

19.187 

21.928 

24.669 

27.41 

30-151 

33  152 

35-633 

4!.ii5 

49 

5.7I4 

12.913 

17.142 

19.999 

22.856 

25-713 

28.57 

31-427 

34.284 

37-I41 

42.855 

5° 

5-95° 

14.28 

17-85 

20.825 

23.8 

26.775 

29-75 

32-725 

35-7 

38-675 

44-62-5 

6.180 

14-832 

18.54 

21.665 

24.76 

27-855 

30.95 

34.045 

37.08 

40.205 

46.425 

52 
53 

6.432 

6.684 

!5-437 
16.041 

19.296 
20.052 

22.512 
23-394 

25.728 
26.736 

28.944 
30.078 

32.16 
33-42 

35.376 
36.762 

38.592 
40.104 

41.808 
43-446 

48  240 
50.130 

54 

6.940 

16.656 

20.82 

24.29 

27.76 

31-23 

34-7 

38-17 

41.64 

45-ii 

5*-°5 

7.198 

17-275 

21.594 

25.193 

28.792 

32.391 

35-99 

39  •  589 

43-188 

46.787 

53.985 

I 

7.462 
/•732 
8.006 

17.909 
iS-557 
19  214 

22.386 
23.196 
24.018 

26.117 
27.062 
28.021 

29  848 
30.928 
32.024 

33-579 
34-794 
36.027 

3sJ:3S 

40.03 

41.041 
42.526 
44-033 

44-772 
46.392 
48.036 

48.503 
50.258 
52.039 

55.965 
57-99 
60.045 

g 

8.284 
8.566 

19.902 
20.558 

24.852 
25.698 

28.964 

29.981 

33-136 
34-264 

37-278 
38.547 

41.42 
42.83 

47-113 

48.704   53.846 
51.396  !  55-679 

62.13 
64.245 

HANDY   TABLES. 


49 


OH 

X! 
H 

5T    ^ 

>    o 

X      c/) 

O 


POINTS  OF  CUT-OFF. 

« 

8*  o*^ 

•s'S'ss- 

22^1 

1222 

2222 

•^  CO  CO  CO 

oooo 

! 

00 

5-5-5-3- 

H1?? 

CO  CO    t^sO 

???? 

CO  CO  IN     « 

S 

s 

vo  VO   >0  •*• 

cTctcTc? 

UK 

e?  c?  r?  N 

10  •*  ro  co 
co  co  co  co 
n  M  ci  w 

w  ct  «  n 

8 

«   t^O    10 

ro  co  ro  co 

HE.co 

CO  CO  CO  CO 

vo    to  •«•  CO 

CO  CO  CO  ro 

IRIS 

M 

8 

M    M    OOO 

^^^2 

2^8^ 

SvTSS 

11^8 

ISSI 

* 

T  T  "T  * 

i 

SHS 

iS^S 

10  10  10  10 

fHs 

^SSI 

???s 

! 

1 

S 

ESjoS 

1411 

•*  «  o  ^ 

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HANDY  TABLES.  $7 

XX. 

HIRN'S  ANALYSIS. 


DATA  AND  RESULTS. 

Test  of  Steam-engine  made  by at 

Kind  of  engine Diam.  cylinder Length  stroke.. 

Diam.  piston-rod Vol.  cylinder,  crank  end Vol.  head  end. 

Vol.  clearance,  cu.  ft.,  head Clearance  in  per  cent  of  stroke. 

"  ••       crank "  "  "     .. 

Boiler-pressure  by  gauge Barometer 

Boiler-pressure  absolute Boiling  temp.,  atmos.  pressure . . 

Revolutions  per  hour ...     Steam  used  during  run,  Ibs 

Quality  of  steam  in  steam-pipe Quality  of  steam  in  steam-chest. 

Quality  of  steam  in  compression Quality  of  steam  in  exhaust. . . . 

Weight  of  condensed  steam  per  hour 

Pounds  of  wet  steam  per  stroke Head Crank. . . . 

Temperatures  condensed  steam 

Temperatures  condensing  water,  cold Hot 

Pounds  of  condensing  water,  per  hour Per  stroke 


SYMBOLS. 

To  denote  different  portions  of  the  stroke,  the  following  subscripts  are 
used  : 

Admission  (a);  expansion  (3);  exhaust  (c);  compression  (d). 

To  denote  different    events    of    the    stroke,    the   following  sub-numbers 
are  used : 

Cut-off  (i);   release  (2);   compression,  beginning  of  (3);   admission,  begin- 
ning of  (o);  in  exhaust  (5). 

Quality  of  steam  denoted  by  X. 

Cut-off,  crank  end  per  cent  of  stroke Release,  crank  end 

Cut-off,  head  end  per  cent  of  stroke Release,  head  end 

Compression,  crank  end  per  cent  of  stroke.. . .     Lbs.  steam  per  I.  H.  P 

Compression,  head  end  per  cent  of  stroke.. . . "   Lbs.  steam  per  brake  H.  P 

I.  H.  P Brake  horse-power 


HANDY   TABLES. 


XX.— {Continued) 

DATA   AND    RESULT? 

PER  100  STROKES. 
Engine.  Date 


.189 


QUANTITIES. 

SYMBOL. 

FORMULA. 

RESULTS 

1 

•3 

2 
u 

M 

G 
K 
Q 

Q* 

y0  (Wt.  per  cu.  ft.) 

Weight  of  steam  in  clearance,  Ibs  
Weight  of  steam  total               •> 

Heat  given  to  condensing  water,  B.T.U. 

M(XL-\-S)  

Heat  retained  by  compression,  B.T.U  .. 
External  heat  steam  at  cut-off,  B.T.U... 
Internal  heat  steam  at  cut-off,  B.T.U.  .. 

Cylinder  loss  during  admission,  B.T.U. 
Loss  sensible  heat  during  expansion  — 

Internal  heat  after  expansion  

Wo  +  -£o-°. 

£+^| 

(M  -f-  M0)(Sl      «S"a)                     .... 

Cylinder  loss  during  expansion,  B.T.U. 

(M+M)S 

H 

Internal  heat  at  compression  

». 

™£ 

Heat  delivered  from  condenser  

Heat  carried  off  in  exhaust 

If* 

Q. 

Q< 

H' 

Q* 
Q 

B 
D 
D' 

M(XL&  +  S6)  (per  calorimeter)  — 

Cylinder  loss,  exhaust,  B.T.U  

**                   M                    M                       «« 

Sensible  heat,  gain  during  compression. 
Internal  heat  at  admission    .... 

•»«-*-& 

Cylinder  loss  during  compression,  B.T.U. 
Heat  admitted  

Heat  discharged  and  external  work.  
Loss  

ffe  -f-  K-\-  total  W-t-  778 

O  —  B 

Loss  

Q    -\-Oh-4-O   4-  OA 

HANDY   TABLES. 


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>•  Pereffectiv 
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placement  
Latent  heat  per  pound  of  steam 
British  thermal  units  
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expansion  
Thickness  of  piston,  inches,  to  near 
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Probable  condensation,  hourly,  o 
faces,  pounds  
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&?,',&.  }P«  effectived 

66 


HANDY   TABLES. 


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HANDY  TABLES. 


XXl.--(Conttnue&) 

CONDENSING  ENGINES—  JACKETED  (  VLINDERS—  DRY  SATURATED  STEAM 

POINT  OF  CUT-OFF. 

* 

£•„**"£>!»  £ 

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NON-CONDENSING  ENGINES-UNJACKETED  CYLINDERS-STEAM  SUPERHEATED  SUFFICIENTLY 
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Terminal  pressure,  pounds  per  square  inch..:  (1 
Volume  of  i  Ib.  of  steam,  cubic  feet.  Atmos.  pressure  (r)  (' 
Mechanical  effect  of  i  Ib.  of  steam,  during  expansion,  foot-lbs.  (1 
Units  of  heat  condensed  for  work,  per  Ib.  of  steam  (j 

Total  heat,  British  thermal  )  Saturated  steam  (/ 
units  per  Ib.,  above  32°.  vSteam  superheated  to  prevent 
Fah.,  of  steam  at  pressure  (r)  \  condensation  due  to  work.  ...  (I 

Temperature,  Fah.,  of  superheated  steam,  including  50°  of  }  ,, 
superheat  to  prevent  condensation  due  to  radiation  f 

Degrees  of  superheat,  Fahrenheit...  (^ 

.  rt    

•  u    

iliiili.! 

Mean  pressure,  J  cSshJon^  f°r  back-Pressure  •  •  • 

saurr^inch61^  1  Corrected  for  back-pressure,  cie 
square  mch.  ^  Probable  effective.  .  
Probable  effective  horse-power  ... 
f  By  piston-displacement  
Pounds  of  steam  I  Condensed  in  jacket  
hourly.  ]  Total  
L  Per  effective  horse-power,  

HANDY   TABLES.  OQ 

XXL—  (Continued) 

NON-CONDENSING  ENGINES,  UNJACKETED  CYLINDERS,  STEAM 
SUPERHEATED  SUFFICIENTLY  TO  PREVENT  CONDENSATION. 


j 

POINT  OF  CUT-OFF. 

a 

Full 

»£ 

in 

Str'ke 

H 

M 

\i 

y± 

% 

H 

A 

Probable  effective  horse-power. 

(£) 

150.6 

151  5 

148.8 

*47  5 

150.6 

148.8 

149.8 

I50.I 

19 

Pounds  of  steam  used  j  pfL*// 

Q 

5851 

5539 

3963 

3494 

3328 

3268 

3627 

3925 

47 

hourly,  calculated  by  \   fective 
piston-displacement.  !   j|   p 

(W) 

38.8 

36.6 

26.6 

23-7 

22.1 

22 

24.2 

26.1 

57 

Point  of 
Cut-off. 

Pounds  of 
steam  hourly. 

Effective 
horse-  power. 

Pounds  of  steam 
hourly,  per 
effective 
horse-power. 

Full  stroke. 

5883 
5582 
4°34 
3611 
3506 
3619 
4031 
4480 

177 
178.9 
180.2 
1  88 
202.3 
228.6 
257-3 
321.9 

33-2 
31-2 
22.4 
i9-3 
i7-3 
iS-9 
iS-7 
i3-9 

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